A Fermatean Fuzzy Opportunity Losses-Based Polar Coordinate Distance Method for Artificial Intelligence-Enhanced Custom

Abstract The increasing adoption of artificial intelligence (AI) across industries has also extended to the field of advertising, where AI is being utilized in various aspects of advertisement design. AI bots employing text-to-image techniques have emerged as an effective approach for generating customized print advertisements. Drawing on the principles of Social Cognitive Theory, this study conceptualizes AI as a cognitive decision-support tool that enhances marketers’ learning, creative judgment, and advertising decision-making through iterative feedback and systematic evaluation. This study aims to develop a decision support system (DSS) for designing AI-enhanced custom-made print ads and selecting the best advertisement from among the generated alternatives. A methodological approach comprising four phases is employed, focusing on the production of advertisement alternatives and their ranking using a multi-attribute group decision-making approach. As DSS, the Fermatean fuzzy (FF)-Entropy-opportunity losses (OPLO)-based polar coordinate distance (POCOD) hybrid method is proposed and developed in this research. Decision-maker weights are determined using FF sets. Criteria weights are calculated based on expert opinions through the FF-Entropy method. The aggregation of expert decision matrices is conducted using the FF-weighted partitioned dual Maclaurin symmetric mean (FFWPDMSM) aggregation operator. The AI-enhanced custom-made print ads are ranked using the FF-OPLO-POCOD method. The applicability of the proposed hybrid method is demonstrated in a case study involving the design of advertisements for a dairy product aimed at a hedonic customer base. The results identify Ads-4 as the most effective AI-generated advertisement among the twelve alternatives. Sensitivity and comparative analyses confirm the robustness and consistency of the proposed framework, with the top-ranked alternative remaining unchanged in all but one sensitivity scenario, thereby demonstrating the stability and reliability of the decision-making process. The study concludes by presenting theoretical and practical implications for AI-assisted advertising and marketing decision-making. Introduction Companies utilize advertising to increase sales, build brand awareness, create brand image, and systematically influence consumer behavior [1]. Advertising, particularly in promotional activities, plays a crucial role. In the advertising industry, agencies and media organizations support companies in designing and selecting the most appropriate advertisements. Traditional advertising focuses on broad audiences, often delivering standardized messages [2]. To design advertisements more tailored to a company’s target audience, the concept of custom-made print ads has emerged [3]. Custom-made print ads are designed to deliver a specific message aimed at a particular target audience for a given product or brand [4]. Creativity plays a key role in these ads, aiming to capture the attention of the target audience and stimulate a desire to purchase, prompting them to act. In terms of characteristics, custom-made print ads are more niche compared to traditional advertising [5]. As a result, the process of designing custom-made print ads may involve higher costs. However, because they target more specific audiences, the overall distribution of the advertisement may also incur lower costs. Furthermore, the personalized nature of custom-made print ads contributes to creating advertisements that align more closely with the strategies of the brand and product [6]. Technically, these ads (given their clearer objectives) can more easily achieve high-quality and desired messaging outcomes. In the process of designing custom-made print ads, advertising agencies, and consultants provide more specialized services to support companies. Compared to traditional advertisement design, companies typically face higher costs when developing digital and custom-made print ads [7]. This is particularly challenging for smaller businesses and individual sellers, who may find it difficult to bear the higher costs of developing advertisements specifically tailored to their target audience. Moreover, limited expertise in designing custom-made print advertisements can negatively affect small-scale companies’ ability to gain a competitive advantage. AI (Artificial Intelligence)-supported advertising offers an effective solution by reducing design costs, automating content generation, and enabling the rapid development of personalized advertisements without requiring extensive marketing expertise. From the perspective of Social Cognitive Theory, AI-based tools also facilitate observational learning by enabling small business owners to identify successful advertising patterns and apply these insights to their own campaigns [8]. In addition, AI-generated feedback helps improve marketing knowledge, strengthens self-efficacy in advertising decisions, and supports the refinement of promotional strategies through repeated learning. As a result, AI-supported advertising enables small businesses to enhance advertising effectiveness, respond more quickly to changing customer preferences, and compete more successfully with larger firms despite their limited resources. The rapid development of technology and the increasing use of AI have begun to significantly impact the advertising industry [9, 10]. AI applications, particularly those involving text-to-image and image-to-image approaches for visual design, are becoming increasingly important [11, 12]. The use of AI in the advertising industry offers opportunities for cost-effective solutions [13, 14]. AI applications can serve as a viable alternative in the process of designing custom-made print ads [15]. The main motivation of this research stems from the increasing use of generative AI in advertisement design and the lack of systematic approaches for selecting the most effective advertisement from the numerous alternatives generated by AI. Although AI technologies can rapidly produce personalized custom-made print advertisements, organizations still require structured decision support to identify the alternative that best satisfies advertising objectives and target customer expectations. Accordingly, this study presents an AI-enhanced approach that combines generative AI with a multi-attribute group decision-making framework to support both the creation and evaluation of advertisement alternatives. Within this context, the design and selection of AI-enhanced custom-made print advertisements are formulated as a decision-making problem, enabling a transparent, reliable, and evidence-based advertisement selection process. In literature, decision-making problems are often approached using multi-criteria decision-making (MCDM) methods [16], allowing decision-makers to select the best alternative and rank the options [17]. This study adopts a multi-attribute group decision-making (MAGDM) approach for the design and selection of AI-enhanced custom-made print ads. The research proposes using AI bots [18] for designing custom-made print ads, and the Fermatean fuzzy (FF)-Entropy-opportunity losses (OPLO)-based polar coordinate distance (POCOD) hybrid method is developed and recommended as a decision support system (DSS) for selecting the best advertisement from the designed alternatives. FF sets are adopted because they provide greater flexibility than traditional fuzzy sets in representing experts’ uncertainty and hesitation, thereby enabling more reliable modeling of subjective evaluations in complex advertising selection problems. In addition, the OPLO-POCOD method is selected as the alternative ranking approach because it simultaneously considers opportunity losses between alternatives and ideal reference points in a polar coordinate space. This dual evaluation mechanism provides a more comprehensive assessment than distance-based methods relying on a single measurement perspective. In this hybrid method, FF sets are used to determine the contribution levels of decision-makers in the decision-making process. The FF-Entropy method, extended with FF sets, is utilized to calculate the weights of the selection criteria for custom-made print ads. Furthermore, the FF-weighted partitioned dual Maclaurin symmetric mean (FFWPDMSM) aggregation operator [19] is employed to aggregate expert evaluations. The FFWPDMSM operator is selected because it effectively captures the interrelationships among criteria while accommodating the uncertainty and hesitation inherent in experts’ linguistic assessments under the FF environment. To select the best alternative from the AI-generated custom-made print ads, the FF-OPLO-POCOD method [20], extended with FF sets, is applied. This hybrid method enables more precise calculations of the importance levels of both experts and criteria, leading to more robust results in the ranking of alternatives. Research Gap Existing studies have primarily focused on the capability of AI to generate creative advertising content, improve personalization, and automate design processes. However, comparatively limited attention has been paid to the systematic evaluation and selection of AI-generated advertisement alternatives. In practice, organizations often generate multiple advertisement designs using AI tools, yet selecting the most effective alternative remains a complex decision-making problem involving multiple evaluation criteria, uncertainty in expert judgments, and differing stakeholder perspectives. Consequently, there is a need for a structured decision support framework that can objectively evaluate AI-generated advertisements and identify the most appropriate alternative. Furthermore, the existing literature has rarely integrated Social Cognitive Theory with AI-assisted advertisement evaluation and advanced multi-attribute group decision-making approaches. Previous studies generally emphasize AI as a content generation technology, while overlooking its role as a cognitive decision-support tool that facilitates learning, expert judgment, and adaptive decision-making. In addition, no previous study has combined FF sets, the FF-Entropy weighting method and the OPLO-POCOD ranking method within a unified framework for evaluating AI-generated custom-made print advertisements. Addressing these gaps, the present study proposes a novel FF-Entropy-OPLO-POCOD hybrid decision support system that integrates generative AI with Social Cognitive Theory and MAGDM to provide a systematic, reliable, and uncertainty-aware framework for advertisement design and selection. Research Aims and Contributions The primary aim of this study is to develop a DSS for AI-enhanced advertisement design by integrating AI technologies with a MAGDM framework. Specifically, the study focuses on the generation of custom-made print advertisements using AI bots through a text-to-image approach and the selection of the most appropriate advertisement from the generated alternatives using the proposed FF-Entropy-OPLO-POCOD hybrid method. By combining AI-assisted creative content generation with advanced decision-making techniques, the proposed framework supports organizations in producing personalized advertisements while enabling systematic, transparent, and reliable advertisement selection. To achieve this objective, the study develops a comprehensive hybrid methodology in which FF sets are employed to represent experts’ uncertain linguistic assessments and determine their contribution levels, while the FF-Entropy method is used to calculate objective criterion weights. Expert evaluations are aggregated using the FFWPDMSM operator, which was selected because it can capture the interrelationships and interactions among criteria while simultaneously accommodating the uncertainty inherent in experts’ linguistic evaluations. Unlike conventional aggregation operators that typically assume criterion independence, the FFWPDMSM operator preserves dependency structures within criterion groups, resulting in a more realistic representation of complex decision-making problems. Subsequently, the FF-OPLO-POCOD method is applied to rank the AI-generated advertisement alternatives. The proposed framework is validated through a real-world case study involving dairy products in Türkiye, and its robustness and reliability are examined through sensitivity and comparative analyses. This research makes several noteworthy contributions to advertising, marketing, and decision science literature. First, it introduces the FF-Entropy-OPLO-POCOD hybrid method as a novel DSS for AI-enhanced advertisement design and selection. Second, it demonstrates the practical feasibility of employing AI boots to generate customized print advertisements using a text-to-image approach, thereby illustrating how generative AI can support creative advertising processes. Third, the study represents the first integration of the OPLO-POCOD method with FF sets, extending the applicability of this ranking approach to uncertain group decision-making environments. Fourth, the proposed framework combines advanced fuzzy modeling, objective weighting, expert aggregation, and alternative ranking into a unified MAGDM methodology, providing a comprehensive decision-making framework for advertisement evaluation. Finally, the empirical case study confirms the applicability of the proposed method in practice and shows that it produces robust and consistent results, highlighting its potential to assist organizations in designing and selecting AI-supported advertisements more effectively. The developed framework may also be adapted to other advertisement design and marketing decision problems, providing a foundation for future research on AI-assisted decision support systems. Research Novelty and Methodological Advantages The novelty of this study lies in the integration of generative AI with an advanced MCDM framework to support both the generation and systematic selection of AI-enhanced custom-made print advertisements. Unlike existing studies, the proposed framework unifies these two processes within a DSS. From a methodological perspective, this research presents the first integration of the OPLO-POCOD method with FF sets, enabling the ranking method to operate effectively in uncertain group decision-making environments. In addition, the proposed FF-Entropy-OPLO-POCOD hybrid method combines FF sets, FF-Entropy, the FFWPDMSM aggregation operator, and the FF-OPLO-POCOD ranking approach into a comprehensive framework that simultaneously addresses uncertainty. The proposed approach also offers a more comprehensive representation of uncertainty, considers interrelationships among criteria during expert aggregation, and evaluates alternatives by jointly incorporating opportunity losses and distances from ideal reference points. These methodological advantages provide a robust decision support framework for selecting AI-generated custom-made print ads and demonstrate its potential applicability to a wide range of AI-assisted marketing and advertising decision problems. Organization of the Study This paper consists of six sections. In Sect. "Literature review", information is provided about custom-made print ads and their design using AI enhancements. Section "Methodological Framework" presents the research methodology, which is divided into four phases, each explained in detail. Section "Case Study: Development and Selection of AI-Enhanced Custom-Made Print Ads Targeting Hedonistic Consumers for a Dairy Product" focuses on the case study application, where information about the case study is provided and the methodology of the case study implementation is described. Additionally, each phase of the research methodology is applied step by step, and the sensitivity and comparative tests are presented at the end of this section. In Section "Results and Implications", the research findings and their implications are discussed. Section "Conclusion" serves as the conclusion, where a general assessment is made, along with the limitations of the study and recommendations for future research. Literature Review Generating Custom-Made Print Ads Using Artificial Intelligence The emergence of Web 3.0 has profoundly altered how individuals seek and consume information tailored to their specific preferences. Recognizing the significance of personalization, businesses have aimed to deliver more sophisticated and precise information services to meet individual needs [21]. Marketers are increasingly adopting digital technologies to reach consumers more effectively and deliver more personalized advertising experiences [22, 23]. This shift creates new opportunities to develop more innovative and personalized advertising strategies, particularly in digital environments [24]. AI has become an integral part of everyday life and is now widely used across many industries. In marketing, AI supports product development, enables personalized advertising, improves customer targeting, and helps identify consumer behavior patterns. As a result, it has become an important tool for delivering more personalized and effective marketing strategies [25]. The rapid growth of social media and digital platforms has transformed how consumers interact with brands, making personalized communication increasingly important. Since 2020, advances in AI have further strengthened this trend by enabling the analysis of large volumes of consumer data and supporting the design, management, and optimization of advertising campaigns. By identifying patterns in online behavior, social media activity, and purchasing habits, AI helps marketers better understand consumer preferences and deliver more targeted and personalized advertisements. By combining AI with personalized marketing strategies, businesses can better understand customer preferences and develop targeted offers that provide more relevant and individualized experiences [26]. By analyzing large volumes of customer data, AI helps companies understand consumer preferences and provide personalized experiences at scale, enhancing the overall customer journey [25]. AI also can identify consumer behavior patterns and help marketers deliver advertisements to the right audience at the right time. By continuously analyzing user data, AI improves the relevance and effectiveness of advertising campaigns, leading to higher customer engagement, improved conversion rates, and better marketing performance [25]. Companies develop various advertising strategies to strengthen their marketing policies [27]. These strategies may focus on the product itself, the target audience, or specific themes. When companies present their targeted advertising strategies as specially designed ads, these are referred to as custom-made print ads. This strategy involves creating advertisements tailored specifically to individual customers [28]. Custom-made print ads allow for the preparation of advertisements suited to the target audience, fostering focused messaging. Additionally, they contribute to strengthening brand identity by creating a lasting image and original designs. Given their tailored nature, custom-made print ads also play a direct role in creating a visual impact that significantly enhances purchasing attitude [29]. The process of designing custom-made print ads differs from traditional advertising approaches. While traditional ad design prioritizes product promotion, custom-made print ad design adopts a multidimensional approach. This involves analyzing the target audience to determine their demographic characteristics, interests, and needs [30]. Furthermore, to encourage call-to-action behavior among consumers, the message must be accurately defined and designed with a clear purpose [31]. Moreover, visual elements such as visual design [32], color contrast [33], the placement of images, and text in the advertisement are critical factors that enhance ad effectiveness [34]. From a technical standpoint, the quality of the print, resolution levels, and the use of specialized printing techniques are also important. Designing custom-made print ads requires a professional approach. Advertising agencies are ideal professionals for creating custom-made print ads. In computer-assisted custom-made print ad design, graphic designers play a key role. Freelance graphic designers provide individual services to companies, aiding in the creation of custom-made print ads, while graphic design agencies offer professional services. Within companies, marketing departments and teams also contribute to the creation of custom-made print ads. The advancement of information technology and the growing capability of AI in generating visual materials have opened new avenues for using AI as an ideal tool in the design of custom-made print ads [35]. AI bots, particularly those that offer text-to-image and image-to-image design capabilities [11], present an alternative, cost-effective method for companies seeking to create ads with little to no expense. Specifically, the text-to-image approach facilitates the design of alternative ads for well-defined custom-made print ad campaigns, streamlining companies’ marketing and advertising processes [36]. This research examines the AI-enhanced custom-made print ad design process and proposes the use of AI to create cost-effective ads. Additionally, it suggests that the problem of selecting the best custom-made print ad from AI-generated alternatives can be addressed using an MCDM approach, which supports the decision-making process. Developing a decision model and defining criteria within that model is crucial for solving the custom-made print ads selection problem. The identification of appropriate criteria and the inclusion of expert opinions significantly improve the selection process. Thus, the methodological approach and DSS proposed in this study offer an alternative solution for the design and selection of custom-made print ads. Recent Advances in Fuzzy-Based Decision Support Systems DSS development increasingly relies on advanced fuzzy environments to model uncertainty and ambiguity in complex decision-making problems. Among these environments, FF sets have attracted considerable attention because of their superior ability to represent experts’ uncertainty and hesitation compared with conventional fuzzy extensions. Owing to this flexibility, FF sets have been widely integrated with MCDM methods to improve the reliability of decision support algorithms. Recent studies demonstrate the growing applicability of FF sets across a wide range of decision-making contexts. For example, Seikh and Chatterjee [37] proposed an FF-based hybrid framework integrating SWARA (Stepwise Weight Assessment Ratio Analysis), the Best–Worst Method (BWM), and VIKOR (VIšeKriterijumska Optimizacija I Kompromisno Rešenje) for sustainable electronic waste management. In the renewable energy domain, Seikh and Chatterjee [38] employed interval-valued FF sets within a MAGDM framework by integrating SWARA and ARAS (Additive Ratio Assessment) to evaluate renewable energy alternatives. Similarly, Seikh and Mukherjee [39] combined FF sets with the CRADIS (Compromise Ranking of Alternatives from Distance to Ideal Solution) method to support online shopping decisions. More recently, Chatterjee and Seikh [40] developed a hybrid FF-RANCOM (Ranking Comparison)-AROMAN (Alternative Ranking Order Method Accounting for Two-Step Normalization) framework for evaluating wastewater reuse alternatives in industrial treatment systems. Likewise, Yalçın et al. [41] integrated FF sets with the SIWEC (Simple Weight Calculation) and ARLON (Alternative Ranking using Two-Step Logarithmic Normalization) methods to assess transportation performance, while Yalçın et al. [42] combined FF-RANCOM with the Symmetry Point of Criterion (SPC) method to evaluate sustainability performance. These studies collectively demonstrate that FF sets provide an effective environment for handling uncertainty in complex group decision-making problems. In parallel with the development of advanced fuzzy environments, aggregation operators have become an essential component of contemporary decision support systems because they enable the integration of multiple experts’ opinions while preserving the characteristics of uncertain information. Recent research has highlighted the effectiveness of aggregation operators in diverse application areas. For instance, Abosuliman et al. [43] integrated aggregation operators with neural networks for nanosensor selection under fuzzy environments. Zhang et al. [44] employed linguistic aggregation operators to support robotic motion simulation, whereas Nawaz et al. [45] demonstrated the usefulness of aggregation operators in improving surgical decision-making processes. These studies indicate that appropriate aggregation mechanisms play a crucial role in enhancing the reliability and robustness of group decision-making models. Beyond FF environments, numerous fuzzy extensions have also been developed to improve decision-making under uncertainty. These include spherical fuzzy sets [46], Pythagorean fuzzy sets [47], single-valued neutrosophic sets [48], intuitionistic fuzzy sets [49], bipolar neutrosophic sets [50], picture fuzzy sets [51, 52], q-rung orthopair fuzzy sets [53], and fractional fuzzy sets [54]. The increasing diversity of these fuzzy environments reflects the continuous effort to develop more flexible and accurate decision support methodologies capable of handling uncertainty in real-world applications. Although previous studies have demonstrated the effectiveness of FF sets and aggregation operators in various MCDM problems, their application to AI-enhanced advertisement design and selection remains largely unexplored. Existing research has primarily focused on traditional engineering, sustainability, logistics, healthcare, and energy applications, with limited attention given to advertising decision-making supported by generative AI. Furthermore, no previous study has integrated FF sets, the FF-Entropy weighting method, the FFWPDMSM aggregation operator, and the OPLO-POCOD ranking method within a unified MAGDM framework for evaluating AI-generated custom-made print advertisements. The present study addresses this gap by developing a comprehensive hybrid decision support system that combines uncertainty modeling, objective criterion weighting, expert opinion aggregation, and alternative ranking to support reliable and transparent AI-assisted advertisement selection. Methodological Framework The methodological framework developed in this study for designing AI-enhanced custom-made print advertisements and selecting the most appropriate advertisement is illustrated in Fig. 1. The framework consists of four sequential phases, each addressing a specific stage of the decision-making process. Phase 1 focuses on AI-assisted advertisement generation. At this stage, the product characteristics, marketing objectives, and target customer profile are identified. Based on these inputs, a detailed prompt is developed and submitted to AI bots using a text-to-image approach to generate multiple custom-made print advertisement alternatives. The outcome of this phase is a set of AI-generated advertisements that constitute the decision alternatives. Phase 2 establishes the decision-making framework for advertisement evaluation. The generated advertisements are defined as the alternatives, the evaluation criteria are identified through an extensive literature review and expert consultation, and the expert panel responsible for the assessment process is determined. This phase provides the foundation for the subsequent multi-attribute group decision-making analysis. Phase 3 involves the development and implementation of the proposed FF-Entropy-OPLO-POCOD hybrid decision support system. First, FF sets are employed to represent experts’ linguistic assessments and determine their contribution levels. The FF-Entropy method is then applied to calculate the objective weights of the evaluation criteria, while the FFWPDMSM operator aggregates individual expert judgments into a collective decision matrix. Finally, the FF-OPLO-POCOD method is used to evaluate and rank the AI-generated advertisement alternatives. Phase 4 is dedicated to validating the proposed methodology. Sensitivity analyses are conducted under different scenarios to examine the stability of the ranking results, while comparative analyses with established MCDM methods are performed to evaluate the consistency and reliability of the proposed hybrid framework. These analyses verify the robustness of the developed decision support system and demonstrate its practical applicability in AI-assisted advertisement selection. Phase 1: Creating AI-Enhanced Custom-Made Print Ads Recent advancements in AI and machine learning have enabled the development of sophisticated generative AI techniques and systems capable of producing text, code, images, and other media in response to user inputs [55]. The primary goal of visualization is to present information in a clear, meaningful, and actionable way. Achieving this requires collaboration among domain experts, designers, and developers to create visual solutions that effectively meet user needs, support decision-making, and fit the intended context. AI technologies have rapidly emerged as one of the most disruptive and transformative innovations of our time. AI refers to a suite of algorithms capable of producing content such as text, images, etc. within existing datasets [56]. This technology replicates creative processes traditionally undertaken by humans, shifting AI’s role from an enabler to a highly efficient co-creator. Tools like ChatGPT, Gemini, DALL-E, Midjourney, and AlphaCode have driven exponential growth in user adoption. However, generative AI’s potential to transform knowledge work is even more profound. AI is rapidly being embedded into software platforms, influencing how companies across industries develop products, deliver services, and create value [57]. Generative AI models excel in processing text, producing human-like responses, and generating realistic images. The use of AI in creating and assembling visualizations has a well-established history. Many recommendation systems have been developed to assist creators in selecting visuals, either through rule-based approaches (typically task-oriented) or machine learning techniques [55]. AI is also increasingly permeating professional domains, streamlining and automating tasks [58]. Text-to-image AI systems have become invaluable in design, enabling the creation of original visual content based on natural language descriptions [59]. These systems also provide layout recommendations that improve the consistency between text prompts and generated images. As a result, they simplify the design process and help produce more coherent and visually appealing advertisements [60]. Furthermore, text-to-image AI enables designers to generate personalized visual content directly from natural language prompts. This capability supports creativity, accelerates the design process, and helps produce advertisements that closely reflect the intended concepts and target audience [61]. The integration of AI systems into design practices creates new opportunities for innovation and creative expression. Text-to-image platforms are increasingly used in advertising to generate visual content and promotional designs. As these technologies continue to advance, their role in developing custom-made print advertisements is expected to expand, transforming the future of advertising design [62]. Companies can produce custom-made print ads, one of the parameters shaping their advertising policies, using AI-enhanced methods, differing from the traditional production process. In this study, keywords were generated to define the target customer portfolio for a dairy brand that a company intends to launch. The prompt to be given to the AI for the design of custom-made print ads was prepared descriptively based on these keywords. The prepared prompt was input into the selected AI interfaces, and the production process was repeated multiple times. Different results were obtained with each iteration. This method demonstrates that custom-made print ads for various products can also be produced using an AI-based approach. Phase 2: Developing a Decision Model for AI-Enhanced Custom-Made Print Ads At this phase, the decision model structure is established for the AI-enhanced custom-made print ads selection process. Three key elements are identified in the decision model: experts, criteria, and AI-enhanced ads. Experts are selected from those with expertise and experience in marketing and advertising, with a particular emphasis on their ability to evaluate ads based on the defined selection criteria. During the criteria determination process, factors that directly influence ad selection are identified, and their impact on the selection process is explained and defined. To define the ad alternatives, the text prompts to be input into AI bots are first determined. These text inputs are converted into images, resulting in various ad designs. This process is carried out using different AI bots. Subsequently, alternative ads, along with expert opinions, are incorporated into the decision model. Once the decision model is created, data is collected for the implementation of the FF-Entropy-OPLO-POCOD hybrid method, and the application steps are initiated. Phase 3: Developing a Hybrid Model for AI-Enhanced Custom-Made Print Ads At this phase, the FF-Entropy-OPLO-POCOD hybrid method is developed and presented to address the AI-enhanced custom-made print ads selection problem. First, the preliminaries for FF set operations are explained. Then, the steps of the FF-Entropy-OPLO-POCOD hybrid method are outlined sequentially. Fermatean Fuzzy Sets Definition 1. An FF sets \(\widetilde{\mathfrak{J}}\) defined over a non-empty set \(\mathfrak{K}\) can be expressed as follows: \(\widetilde{\mathfrak{J}}=\left\{\langle \mathfrak{k},{\delta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right),{\beta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)|\mathfrak{k}\in \mathfrak{K}\rangle \right\},\) where\({\delta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right):\mathfrak{K}\to \left[\text{0,1}\right] , {\beta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right):\)\(\mathfrak{K}\to \left[\text{0,1}\right], \text{a}\text{n}\text{d} {\gamma}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)=\)\(\sqrt[3]{1-{\left({\delta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)\right)}^{3}-{\left({\beta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)\right)}^{3}}\). These represent the concepts of MD, NMD, and indeterminacy, respectively [63]. These are explained with the limitation that\({0\le \left({\delta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)\right)}^{3}+{\left({\beta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)\right)}^{3}\le 1\). Herein, it holds true for all elements \(\mathfrak{k}\) in the set\(\mathfrak{K}\). In this paper, it is called FF numbers for elements of the FF sets. Definition 2. An empirical application illustrating the use of FF sets based on the proposed procedures [64]: Let \(\widetilde{\mathfrak{J}}=\left({\delta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right),{\beta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)\right)\), \({\widetilde{\mathfrak{J}}}_{1}=\left({\delta}_{{\widetilde{\mathfrak{J}}}_{1}}\left(\mathfrak{k}\right),{\beta}_{{\widetilde{\mathfrak{J}}}_{1}}\left(\mathfrak{k}\right)\right),\) and \({\widetilde{\mathfrak{J}}}_{2}=\left({\delta}_{{\widetilde{\mathfrak{J}}}_{2}}\left(\mathfrak{k}\right),{\beta}_{{\widetilde{\mathfrak{J}}}_{2}}\left(\mathfrak{k}\right)\right)\) are three FF numbers. The operations are as follows: - (i) \(\begin{aligned}&{\widetilde{\mathfrak{J}}}_{1}\oplus {\widetilde{\mathfrak{J}}}_{2}\\&=\left\{\left(\begin{array}{l}\sqrt[3]{\left({\delta}_{{\widetilde{\mathfrak{J}}}_{1}}\left(\mathfrak{k}\right)\right)}^{3}+{\left({\delta}_{{\widetilde{\mathfrak{J}}}_{2}}\left(\mathfrak{k}\right)\right)}^{3}\\-{\left({\delta}_{{\widetilde{\mathfrak{J}}}_{1}}\left(\mathfrak{k}\right)\right)}^{3}{\left({\delta}_{{\widetilde{\mathfrak{J}}}_{2}}\left(\mathfrak{k}\right)\right)}^{3}\end{array},{\beta}_{{\widetilde{\mathfrak{J}}}_{1}}\left(\mathfrak{k}\right) {\beta}_{{\widetilde{\mathfrak{J}}}_{2}}\left(\mathfrak{k}\right)\right)|\mathfrak{k}\in \mathfrak{K}\right\},\end{aligned}\) - (ii) \(\begin{aligned}&{\widetilde{\mathfrak{J}}}_{1}\otimes {\widetilde{\mathfrak{J}}}_{2}\\&=\left\{\left({\delta}_{{\widetilde{\mathfrak{J}}}_{1}}\left(\mathfrak{k}\right) {\delta}_{{\widetilde{\mathfrak{J}}}_{2}}\left(\mathfrak{k}\right),\sqrt[3]{\begin{array}{l}{\left({\beta}_{{\widetilde{\mathfrak{J}}}_{1}}\left(\mathfrak{k}\right)\right)}^{3}+{\left({\beta}_{{\widetilde{\mathfrak{J}}}_{2}}\left(\mathfrak{k}\right)\right)}^{3}\\-{\left({\beta}_{{\widetilde{\mathfrak{J}}}_{1}}\left(\mathfrak{k}\right)\right)}^{3}{\left({\beta}_{{\widetilde{\mathfrak{J}}}_{2}}\left(\mathfrak{k}\right)\right)}^{3}\end{array}}\right)|\mathfrak{k}\in \mathfrak{K}\right\},\end{aligned}\) - (iii) \(\begin{aligned}&\psi \widetilde{\mathfrak{J}}=\\&\left\{\left(\sqrt[3]{1-{\left(1-{\left({\delta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)\right)}^{3}\right)}^{\psi }},{\left({\beta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)\right)}^{\psi }\right)|\mathfrak{k}\in \mathfrak{K}\right\} \text{f}\text{o}\text{r} \psi>0,\end{aligned}\) - (iv) \(\begin{aligned}&{\widetilde{\mathfrak{J}}}^{\psi }=\\&\left\{\left({\left({\delta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)\right)}^{\psi },\sqrt[3]{1-{\left(1-{\left({\beta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)\right)}^{3}\right)}^{\psi }}\right)|\mathfrak{k}\in \mathfrak{K}\right\} \text{f}\text{o}\text{r} \psi>0.\end{aligned}\) Definition 2 is expected to satisfy the following criteria: - (i) \({\widetilde{\mathfrak{J}}}_{1}\oplus {\widetilde{\mathfrak{J}}}_{2}={\widetilde{\mathfrak{J}}}_{2}\oplus {\widetilde{\mathfrak{J}}}_{1},\) - (ii) \({\widetilde{\mathfrak{J}}}_{1}\otimes {\widetilde{\mathfrak{J}}}_{2}={\widetilde{\mathfrak{J}}}_{2}\otimes {\widetilde{\mathfrak{J}}}_{1},\) - (iii) \(\psi \left({\widetilde{\mathfrak{J}}}_{1}\oplus {\widetilde{\mathfrak{J}}}_{2}\right)=\psi {\widetilde{\mathfrak{J}}}_{1}\oplus \psi {\widetilde{\mathfrak{J}}}_{2} \text{f}\text{o}\text{r} \psi>0,\) - (iv) \({\left({\widetilde{\mathfrak{J}}}_{1}\otimes {\widetilde{\mathfrak{J}}}_{2}\right)}^{\psi }={{\widetilde{\mathfrak{J}}}_{1}}^{\psi }\otimes {{\widetilde{\mathfrak{J}}}_{2}}^{\psi } \text{f}\text{o}\text{r} \uppsi>0,\) - (v) \({\psi}_{1}\widetilde{\mathfrak{J}}\oplus {\psi}_{2}\widetilde{\mathfrak{J}}=\left({\psi}_{1}+{\psi}_{2}\right)\widetilde{\mathfrak{J}} \text{f}\text{o}\text{r} {\psi}_{1},{\psi}_{2}>0,\) - (vi) \({\widetilde{\mathfrak{J}}}^{{\psi}_{1}}\otimes{\widetilde{\mathfrak{J}}}^{{\psi}_{2}}={\widetilde{\mathfrak{J}}}^{\left({\psi}_{1}+{\psi}_{2}\right)} \text{f}\text{o}\text{r} {\psi}_{1},{\psi}_{2}>0.\) Definition 3. Let \(\widetilde{\mathfrak{J}}=\left({\delta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right),{\beta}_{\widetilde{\mathfrak{J}}}\left(\mathfrak{k}\right)\right)\) be an FF set over the universe \(\mathfrak{K}\), with the score function (Eq. (1)) and the accuracy function (Eq. (2)) [63], [65]: Definition 4. Let \({\widetilde{\mathfrak{J}}}_{1}=\left({\delta}_{{\widetilde{\mathfrak{J}}}_{1}}\left(\mathfrak{k}\right),{\beta}_{{\widetilde{\mathfrak{J}}}_{1}}\left(\mathfrak{k}\right)\right)\) and \({\widetilde{\mathfrak{J}}}_{2}=\left({\delta}_{{\widetilde{\mathfrak{J}}}_{2}}\left(\mathfrak{k}\right),{\beta}_{{\widetilde{\mathfrak{J}}}_{2}}\left(\mathfrak{k}\right)\right)\) be two FF sets in the universe \(\mathfrak{K}\). Considering the score and accuracy functions denoted as \(\mathfrak{s}\left(\widetilde{\mathfrak{J}}\right)\) and \(\mathfrak{a}\left(\widetilde{\mathfrak{J}}\right)\) for \({\widetilde{\mathfrak{J}}}_{i}(i=\text{1,2})\), the following ordering relationship can be established [63]: - (i) If \(\mathfrak{s}\left({\widetilde{\mathfrak{J}}}_{1}\right)\) > \(\mathfrak{s}\left({\widetilde{\mathfrak{J}}}_{2}\right)\), then \({\widetilde{\mathfrak{J}}}_{1}>{\widetilde{\mathfrak{J}}}_{2}\), - (ii) If \(\mathfrak{s}\left({\widetilde{\mathfrak{J}}}_{1}\right)\) = \(\mathfrak{s}\left({\widetilde{\mathfrak{J}}}_{2}\right)\), \(\mathfrak{a}\left({\widetilde{\mathfrak{J}}}_{1}\right)\) > \(\mathfrak{a}\left({\widetilde{\mathfrak{J}}}_{2}\right)\), then \({\widetilde{\mathfrak{J}}}_{1}\)>\({\widetilde{\mathfrak{J}}}_{2}\), - (iii) If \(\mathfrak{s}\left({\widetilde{\mathfrak{J}}}_{1}\right)\) = \(\mathfrak{s}\left({\widetilde{\mathfrak{J}}}_{2}\right)\), \(\mathfrak{a}\left({\widetilde{\mathfrak{J}}}_{1}\right)\) = \(\mathfrak{a}\left({\widetilde{\mathfrak{J}}}_{2}\right)\), then \({\widetilde{\mathfrak{J}}}_{1}\)=\({\widetilde{\mathfrak{J}}}_{2}\). Definition 5. Let \({\widetilde{\mathfrak{J}}}_{\mathfrak{t}}=\left({\delta}_{{\widetilde{\mathfrak{J}}}_{\mathfrak{t}}}\left(\mathfrak{k}\right),{\beta}_{{\widetilde{\mathfrak{J}}}_{\mathfrak{t}}}\left(\mathfrak{k}\right)\right)\) represent a family of FF numbers, the FFWPDMSM is defined by Eq. (3) [19]: Herein, \(l=\text{1,2},\dots ,{o}_{t}; t=1, 2,\dots ,c\), \(c\) represents the number of partitions, \({o}_{t}\) represents the number of elements in a group, \({C}_{{o}_{t}}^{l}\) represents the binomial coefficient as \({C}_{{o}_{t}}^{l}=\frac{{o}_{t}!}{l!\left({o}_{t}-l\right)!}\), \({k}_{l}\) represents all the \(l\)-tuple combination of \({o}_{t}\), and \({\varpi}_{{k}_{\mathfrak{t}}}\) represents the weight of \({k}_{\mathfrak{t}}\) (\(\mathfrak{t}=\text{1,2},3\dots ,l)\). Novel FF-Entropy-OPLO-POCOD Hybrid Method Based on the FFWPDMSM Aggregation Operator The FF-Entropy-OPLO-POCOD hybrid method has been created to assist in the selection of custom-made print ads. Let \(\left({\mathcal{B}}_{\mathcal{i}}\right)=\left\{{\mathcal{B}}_{1},{\mathcal{B}}_{2},\dots ,{\mathcal{B}}_{\mathcal{I}}\right\}\), where \(\left(\mathcal{i}=\text{1,2},\dots ,\mathcal{I}\right),\) represent the alternatives, \(\left({\mathcal{C}}_{\mathcal{j}}\right)=\left\{{\mathcal{C}}_{1},{\mathcal{C}}_{2},\dots ,{\mathcal{C}}_{\mathcal{J}}\right\}\), where \(\left(\mathcal{j}=\text{1,2},\dots ,\mathcal{J}\right),\) represent the criteria, \(\left({\mathcal{D}}_{\mathcal{k}}\right)=\left\{{\mathcal{D}}_{1},{\mathcal{D}}_{2},\dots ,{\mathcal{D}}_{\mathcal{K}}\right\}\), where \(\left(\mathcal{k}=\text{1,2},\dots ,\mathcal{K}\right),\) indicate the experts participating in the decision-making process. The notations employed in the FF-Entropy-OPLO-POCOD hybrid method are presented in the Appendix (also shown abbreviations). The proposed hybrid method consists of three stages: expert weighting using FF sets, criterion weighting through FF-Entropy, and alternative ranking using FF-OPLO-POCOD. The overall procedure is presented in Fig. 2. The steps of the FF-Entropy-OPLO-POCOD hybrid method are outlined as follows: Stage 1: Determining the weights for each expert utilizing FF sets. Step 1–1: In the first step of Stage 1, information regarding the experts’ qualifications and experience is collected to determine their expertise levels. Based on the expertise assessment scale presented in Table 1, the experts’ expertise levels are expressed using FF numbers. During this process, expert assessments are represented through predefined linguistic terms. Step 1–2: To determine the experts’ weight vector, the FF numbers are transformed into crisp values. For this purpose, the score function \(\left(\mathfrak{s}\left({\widetilde{\mathcal{D}}}_{\mathcal{k}}\right)\right)\) is applied to convert (Eq. (4)) the FF numbers into quantitative values suitable for subsequent calculations: Steps 1–3: To obtain the experts’ weight vector, the crisp values are standardized (Eq. (5)) within the interval ([0,1]). In this step, a linear normalization approach is employed to calculate the normalized weights \(\left(\varpi ={\left[{\varpi}_{\mathcal{k}}\right]}_{\mathcal{K}}\right)\), which are subsequently used in the following stages of the proposed methodology: Stage 2: Determining the weights for each criterion using FF-Entropy. Step 2–1: In the first step of Stage 2, individual evaluation matrices are constructed based on the assessments obtained during face-to-face interviews with the experts \(\left({\mathcal{D}}_{\mathcal{k}}\right)\). The experts evaluate each advertisement alternative \(\left({\mathcal{B}}_{\mathcal{i}}\right)\) with respect to the predefined selection criteria \(\left({\mathcal{C}}_{\mathcal{j}}\right)\), and their judgments are systematically recorded. The scale presented in Table 2 is used throughout this assessment process \(\left({\widetilde{\mathcal{E}}}^{\left({\mathcal{D}}_{\mathcal{k}}\right)}={\left[{{\widetilde{\mathcal{E}}}^{\left({\mathcal{D}}_{\mathcal{k}}\right)}}_{\mathcal{i}\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) where \(\begin{aligned}&{{\widetilde{\mathcal{E}}}^{\left({\mathcal{D}}_{\mathcal{k}}\right)}}_{\mathcal{i}\mathcal{j}}=\left({\delta}_{{{\widetilde{\mathcal{E}}}^{\left({\mathcal{D}}_{\mathcal{k}}\right)}}_{\mathcal{i}\mathcal{j}}}\left(\mathfrak{k}\right),{\beta}_{{{\widetilde{\mathcal{E}}}^{\left({\mathcal{D}}_{\mathcal{k}}\right)}}_{\mathcal{i}\mathcal{j}}}\left(\mathfrak{k}\right)\right)\\& \left(\mathcal{i}=1,\dots , \mathcal{I};\mathcal{j}=1,\dots ,\mathcal{J};\mathcal{k}=1,\dots ,\mathcal{K}\right)\end{aligned}\): Step 2–2: The individual evaluation matrices are aggregated using the FFWPDMSM aggregation operator (Eq. (6)), taking the experts’ weight vector into account. As a result, an aggregated decision matrix \(\left(\widetilde{\mathcal{E}}={\left[{\widetilde{\mathcal{E}}}_{\mathcal{i}\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) expressed in FF numbers is obtained, which serves as the initial decision matrix for the subsequent FF-Entropy weighting process: herein, \(l=\text{1,2},\dots ,{o}_{t}; t=1, 2,\dots ,c\), while \(c\) represents the number of partitions, \({o}_{t}\) represents the number of elements in a group, \({C}_{{o}_{t}}^{l}\) represents the binomial coefficient as \({C}_{{o}_{t}}^{l}=\frac{{o}_{t}!}{l!\left({o}_{t}-l\right)!}\), \({k}_{l}\) represents all the \(l\)-tuple combination of \({o}_{t}\), \({\varpi}_{\mathcal{k}}\) represents the weight of \(\mathcal{k}=\left(\text{1,2},3\dots ,l\right)\). Step 2–3: In this step, the aggregated FF numbers are transformed (Eq. (7)) into crisp values using the score function \(\left(\mathfrak{s}\left({\widetilde{\mathcal{E}}}_{\mathcal{i}\mathcal{j}}\right)\right)\). This transformation converts the decision matrix from the Fermatean fuzzy environment into a crisp form \(\left(\mathcal{E}={\left[{\mathcal{E}}_{\mathcal{i}\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\), enabling the subsequent objective weighting calculations: Step 2–4: In this step, the crisp decision matrix is normalized (Eq. (8)) to transform all values into the interval ([0,1]), thereby ensuring comparability among the evaluation criteria prior to the entropy-based weighting process \(\left(\mathcal{F}={\left[{\mathcal{F}}_{\mathcal{i}\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\): Step 2–5: In this step, the entropy values of the evaluation criteria are calculated (Eq. (9)) to measure the amount of information and uncertainty associated with each criterion. Herein, \(\alpha ={\left(\text{ln}\left(\mathcal{I}\right)\right)}^{-1}\): Step 2–6: The degree of differentiation for each criterion \(\left(\mathcal{H}={\left[{\mathcal{H}}_{\mathcal{j}}\right]}_{\mathcal{J}}\right)\) is calculated (Eq. (10)) based on the entropy values, reflecting the discriminating power and informational contribution of each criterion to the decision-making process: Step 2–7: The normalized criterion weights \(\left(\mathfrak{w}={\left[{\mathfrak{w}}_{\mathcal{j}}\right]}_{\mathcal{J}}\right)\) are determined (Eq. (11)) based on the calculated degrees of differentiation: Stage 3: Establishing the rankings of alternatives through the application of the FF-OPLO-POCOD method: Step 3–1: In the first step of Stage 3, the best (ideal) values for each criterion \(\left(\mathcal{L}={\left[{\mathcal{L}}_{\mathcal{j}}\right]}_{\mathcal{J}}\right)\) are identified (Eq. (12)). These values serve as the reference points for the subsequent calculations in the FF-OPLO-POCOD ranking procedure: Step 3–2: The loss values \(\left(\mathcal{M}={\left[{\mathcal{M}}_{i\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) for each alternative are determined (Eq. (13)) by measuring the deviation of their performance from the corresponding best (ideal) values for each criterion: Step 3–3: The ordered pair values \(\left(\mathcal{N}={\left[{\mathcal{N}}_{i\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) are constructed (Eq. (14)) by combining the best (ideal) values and the corresponding loss values for each criterion: Step 3–4: The best ordered pair values \(\left(\mathcal{O}={\left[{\mathcal{O}}_{\mathcal{j}}\right]}_{\mathcal{J}}\right)\) are identified (Eq. (15)) to establish the ideal reference points for each criterion: Step 3–5: The distance values \(\left(\mathcal{P}={\left[{\mathcal{P}}_{i\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) between each alternative and the corresponding best ordered pair values are calculated (Eq. (16)) to measure the relative performance of the alternatives: Step 3–6: The distance values \(\left(\mathcal{Q}={\left[{\mathcal{Q}}_{i\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) are weighted (Eq. (17)) using the criterion weight vector: Step 3–7: The weighted distance values are aggregated (Eq. (18)) to obtain the total distance value \(\left(\mathcal{R}={\left[{\mathcal{R}}_{i}\right]}_{\mathcal{I}}\right)\) for each advertisement alternative: Step 3–8: The degree of opportunity loss values \(\left(\mathcal{S}={\left[{\mathcal{S}}_{i}\right]}_{\mathcal{I}}\right)\) are calculated (Eq. (19)) for each advertisement alternative to quantify the overall performance loss relative to the ideal solution: Step 3–9: The percentage of opportunity achievement values \(\left(\mathcal{T}={\left[{\mathcal{T}}_{i}\right]}_{\mathcal{I}}\right)\) are calculated (Eq. (20)) for all advertisement alternatives. Based on these values, the alternatives are ranked, and the advertisement with the highest percentage of opportunity achievement is identified as the optimal AI-enhanced custom-made print advertisement: The algorithmic steps of the FF-Entropy-OPLO-POCOD hybrid model are outlined in Table S.1 in Supplementary Materials. Phase 4: Robustness and Consistency Tests Sensitivity analyses are scenario-based, where the method is reapplied according to the prepared scenarios, and the results are compared with the original outcomes to evaluate the reliability of the findings. To further evaluate the consistency of the FF-Entropy-OPLO-POCOD hybrid model, different methods are employed for comparativeness. The differences and similarities in the rankings of alternatives are observed to form conclusions regarding the model’s reliability. Case Study: Development and Selection of AI-Enhanced Custom-Made Print Ads Targeting Hedonistic Consumers for a Dairy Product In this paper, the problem of designing AI-enhanced custom-made print ads for a dairy product in Türkiye and selecting the best advertisement is addressed. The dairy company aims to create advertisements to market its dairy products and wishes to identify the most effective ad. The target audience of the dairy company consists of hedonic consumers, who are more likely to make purchase decisions based on enjoyment rather than only on functional product features. Therefore, the ads prompts were prepared to reflect these preferences by emphasizing emotional appeal, attractive visuals, and enjoyable consumption experiences. To capture the attention of this customer segment and increase sales, the company seeks to prepare advertisements at minimal cost while determining the best advertisement. This case study is created, and the four phases of the methodology presented in this paper are applied and explained sequentially. Application Phase 1: Creating AI-Enhanced Custom-Made Print Ads for a Dairy Product In the creation of AI-enhanced custom-made print ads, text-to-image technology was utilized through various AI platforms. The selected AI tools include Microsoft Copilot AI, Leonardo AI, Stable Diffusion AI, and ImagineArt AI, all of which support high-quality text-to-image generation. These platforms were selected because of their widespread use, accessibility, ease of use, and ability to generate diverse and customizable visual content suitable for advertising applications. Compared with many other AI image-generation tools, they offer a practical balance between image quality, prompt responsiveness, and creative flexibility. Visual outputs were generated by submitting identical prompts to each platform. Although the same prompts were used, each AI tool produced distinct advertisement designs, providing a diverse set of alternatives for the subsequent multi-attribute group decision-making process. This characteristic suggests that these AI-enhanced tools not only offer the potential to generate a wide range of design options but also possess creative capabilities that can enhance the personalization of advertisements. Prior to generating the advertisements, the prompt was systematically developed to ensure consistency across all AI platforms. The prompt preparation process involved defining the product category, identifying the target customer profile, and specifying the desired advertising message and visual characteristics. These elements were integrated into a single standardized prompt to ensure that all AI tools generated advertisements under identical input conditions, thereby enabling a fair and consistent comparison of the resulting alternatives. In the case study of this research, the identified characteristics were employed to describe the custom-made print ads intended for AI-enhanced production, resulting in the preparation of the following prompt: “A custom-made print ads for a milk product that is aimed at customers who are pleasure-oriented, shop with their emotions and are satisfied with it, enjoy consumption and shopping, are interested, curious, care about emotional experiences, tend towards products or brands that can provide entertainment, pleasure, enjoyment, fantasy, and dream creation, reward themselves with the products they buy, and tend to consume for conspicuous purposes.”. The qualities of the distinct visual outputs generated autonomously differ based on the skills and capabilities of the employed AI interfaces. When visually successful results were achieved, further alternatives were developed. Although identical text prompts were used, different AI tools produced results characterized by diverse styles. This variation extended beyond mere stylistic differences; it was also evident in the skill and expertise exhibited in the design of the visual products. Application Phase 2: Developing a Decision Model for AI-Enhanced Custom-Made Print Ads for a Dairy Product Identification of Experts To apply the proposed FF-Entropy-OPLO-POCOD hybrid method for selecting AI-enhanced custom-made print advertisements, the components of the decision model must first be clearly defined. Among these components, the expert panel plays a pivotal role, as the quality and reliability of the decision-making process largely depends on expert knowledge and experience. Therefore, the expert group was intentionally composed of both academics and practitioners with substantial expertise in marketing, advertising, and brand management to ensure a balanced evaluation from theoretical and practical perspectives. For this application, nine experts participated in the evaluation process. The first two experts are professors specializing in marketing, each with more than twenty years of academic and research experience. The remaining seven experts hold managerial positions in the marketing and advertising industry. Specifically, the third expert is an advertising and public relations manager with 13 years of experience, the fourth is a brand and marketing communication manager with seven years of experience, the fifth is a marketing coordinator with 10 years of experience, the sixth is an executive creative director with 20 years of experience, the seventh is a marketing manager with nine years of experience, the eighth is an advertising director with five years of experience, and the ninth is a marketing specialist with five years of experience. The profiles of all experts are summarized in Table 3. The expert evaluation process was conducted individually to avoid potential bias arising from group influence or dominant opinions. Each expert was provided with the AI-generated advertisement alternatives, the evaluation criteria, and detailed assessment instructions. The experts independently assessed each advertisement using the predefined linguistic evaluation scale based on FF sets. After the individual evaluations were completed, the collected assessments were converted into FF numbers and subsequently aggregated using the FFWPDMSM operator to construct the collective decision matrix for the proposed hybrid decision support system. This procedure ensured consistency, preserved the independence of expert judgments, and enabled the integration of diverse professional perspectives into the final decision-making process. Criteria Set Twelve criteria have been identified for determining the best advertisement among the AI-enhanced Custom-Made Print Ads alternatives. These criteria serve as reference points for experts when evaluating advertisements. The criteria included in the decision model are as follows: - Level of visual appeal \(\left({\mathcal{C}}_{1}\right)\) − The visual element is one of several components, such as the logo, body copy, and headline, that together form an advertisement [67]. To capture consumer attention, a print advertisement must possess features that make it visually appealing. Among these attributes, visual appeal plays a critical role [68]. The visual appeal of an advertisement significantly influences its ability to attract and engage the target audience. If an advertisement fails to capture attention, potential customers may be lost. Therefore, it is essential that the ad immediately captures consumer attention and raises awareness of the products being promoted [69]. Within the scope of this research, “level of visual appeal” has been identified as a key criterion for evaluating “AI-enhanced custom-made print advertisements”. - Level of generating interest \(\left({\mathcal{C}}_{2}\right)\) − When designing a poster, marketers must carefully consider the information to include to effectively convey the product’s benefits after capturing the consumer’s attention. Consumers are typically willing to invest time in reading the advertising message in detail or examining the poster. If marketers can demonstrate that the product addresses a particular problem and clearly explain its features and benefits, they can successfully generate interest among the target audience [70], [71]. Accordingly, the “level of generating interest” has been selected as one of the evaluation criteria in this research. - Level of purchase desire generation \(\left({\mathcal{C}}_{3}\right)\) − One of the primary objectives of advertising is to encourage consumers to purchase a product by communicating its value in a compelling and persuasive manner. Effective advertisements should capture consumers’ attention, create emotional engagement, and strengthen their intention to buy [70, 72]. When an advertisement successfully addresses consumers’ needs and expectations, it increases their motivation to choose the advertised product [71]. For this reason, the level of purchase desire generation was identified as one of the key evaluation criteria in this study. - Level of call to action \(\left({\mathcal{C}}_{4}\right)\) − An effective advertisement should encourage consumers to act by increasing their willingness to purchase the advertised product or service. Even when an immediate purchase does not occur, a persuasive advertisement can positively influence consumers’ decision-making process and strengthen their future purchase intentions [73]. Ads that create emotional engagement are particularly effective in motivating consumer action [31]. Therefore, the level of call to action was included as one of the key evaluation criteria in this study. - Degree of product-visual compatibility \(\left({\mathcal{C}}_{5}\right)\) − This criterion reflects the level of successful alignment between the visual elements used in the advertisement and the product itself. In product-visual compatibility, the adequacy of the advertisement’s visuals is crucial to ensure that the message conveyed to the target audience is communicated effectively [74]. Therefore, product-visual compatibility plays a critical role in the evaluation process of advertisements. In this context, this criterion is included in the decision-making model. - Level of target audience compatibility \(\left({\mathcal{C}}_{6}\right)\) − The process of creating custom-made print ads involves ensuring that the designed advertisements convey a specific message tailored to a particular target demographic [75]. Thus, the demographic, social, and cultural alignment of the advertisement with the target audience is of paramount importance. Therefore, this criterion is included in the decision-making model during the evaluation process of the advertisements. - Level of purpose reflectiveness \(\left({\mathcal{C}}_{7}\right)\) − This criterion indicates the extent to which the advertisement reflects its intended purpose. In the context of custom-made print ads, each advertisement is designed with a specific objective in mind [2]. Therefore, it is essential for the advertisement to align with this purpose throughout its design. Consequently, the level of purpose reflectiveness is regarded as a critical evaluation criterion. The criteria included in the decision model are assessed by experts, considering the relationship between the advertisement and its intended purpose. - Level of clarity/comprehensibility of image and message \(\left({\mathcal{C}}_{8}\right)\) − Considering the multitude of elements across various modalities, the process of poster creation can pose significant challenges, encompassing fundamental aspects and requirements. One such requirement is the generation of concise and structured taglines based on product information, which is essential for the efficient transmission of messages to consumers [76]. - Level of creativity \(\left({\mathcal{C}}_{9}\right)\) − To create an effective and visually appealing poster, all design elements should work together in a consistent and harmonious manner. Achieving this balance often requires considerable time, creativity, and expertise in design, particularly when developing advertisements for different products and formats [76]. - Level of typography suitability \(\left({\mathcal{C}}_{10}\right)\) − Visual communication design, predominantly rooted in typography, constitutes a significant public art form [77]. Within this framework, “AI-enhanced custom-made print advertisements” is also regarded as a product of art and visual communication design, and in this context, “level of typography suitability” has been selected as one of the evaluation criteria. - Level of color incompatibility \(\left({\mathcal{C}}_{11}\right)\) − The ability of humans to discern images strongly indicates that color compatibility is a factor for realistic image composition. By effectively managing color compatibility, it is possible to enhance the realism of an image composite [78]. In this context, “level of color incompatibility” has been established as a cost-based criterion. - Level of ethical concerns \(\left({\mathcal{C}}_{12}\right)\) − Ethics emerges as a fundamental value within any society [79]. Businesses operating within a society are expected to align their practices with the ethical values and norms of that social environment. Thus, ethical conduct has evolved into a central strategic focus for many organizations in articulating and advancing their brand values [80, 81]. Indeed, ethical principles significantly shape a firm’s services, as well as its relationships with society [82]. This criterion is also identified as a cost type in this model. Identification of AI-Enhanced Custom-Made Print Ads for Dairy Products Custom-made print ads were designed using various AI systems, including Microsoft Copilot AI, Leonardo AI, Stable Diffusion AI, and ImagineArt AI, for a company specializing in dairy production. The details regarding these AI systems are as follows: - Microsoft Copilot AI is an AI-powered image generation tool developed by Microsoft that utilizes DALL·E 3 technology to create images from text prompts. By interpreting users’ textual descriptions, it generates multiple visual alternatives that closely match the intended concepts. Its ability to produce high-quality and detailed images, particularly when provided with well-structured prompts, makes it a suitable tool for creating AI-enhanced advertisement designs. The first seven alternative custom-made print ads (from \({\mathcal{B}}_{1}\) to \({\mathcal{B}}_{7}\)) presented in Fig. 3 were designed using Microsoft Copilot AI. - Leonardo AI is a generative AI platform designed for creating high-quality visual content from text prompts. It enables users to produce detailed images suitable for creative applications such as graphic design, digital art, and advertising. Its capability to generate visually rich and customizable outputs makes it well suited for developing AI-enhanced advertisement alternatives. The 8th alternative custom-made print ads (\({\mathcal{B}}_{8}\)) presented in Fig. 3 were designed using Leonardo AI. - Stable Diffusion AI is an open-source generative AI model that creates high-quality images from text prompts. It is widely recognized for its flexibility, customization capabilities, and ability to generate diverse visual outputs from the same prompt. These features make it an effective tool for producing alternative advertisement designs with varying creative styles. The 9th and 10th alternative custom-made print ads (\({\mathcal{B}}_{9}\) and \({\mathcal{B}}_{10}\)) presented in Fig. 3 were designed using Stable Diffusion AI. - Like other AI-powered tools in the realm of text-to-image generation, ImagineArt AI leverages machine learning techniques to transform user inputs into creative and realistic visual outputs. It caters primarily to artists, designers, and content creators seeking to streamline their creative process or explore new artistic possibilities using AI technology. The 11th and 12th alternative custom-made print ads (\({\mathcal{B}}_{11}\), \({\mathcal{B}}_{12}\)) presented in Fig. 3 were designed using ImagineArt AI. Application Phase 3: Application of the FF-Entropy-OPLO-POCOD Hybrid Method In this case study, the development and selection of AI-enhanced custom-made print advertisements for a dairy product are examined. The primary objective is to demonstrate the practical implementation of the proposed FF-Entropy-OPLO-POCOD hybrid method for identifying the most effective advertisement among AI-generated custom-made print advertisement alternatives. As described in the previous section, the decision-making model consists of nine experts, twelve evaluation criteria, and twelve advertisement alternatives. Based on the data collected through face-to-face interviews with the experts, the stages of the proposed FF-Entropy-OPLO-POCOD hybrid method were implemented sequentially as follows. Stage 1 (Application): Determining the weights for each expert utilizing FF sets: Stage 1 consists of three sequential steps designed to determine the experts’ weights and their contribution levels to the decision-making process. In Step 1–1, the experts qualified to evaluate the custom-made print advertisements were assessed (Table S.2) using the expertise assessment scale presented in Table 1. In Step 1–2, the corresponding FF numbers were transformed (Eq. (4)) into crisp values \(\left(\mathfrak{s}\left({\widetilde{\mathcal{D}}}_{\mathcal{k}}\right)\right)\) to facilitate quantitative analysis (Table S.2). Finally, in Step 1–3, the crisp values were normalized (Eq. (5)) to calculate the experts’ weight vector \(\left(\varpi ={\left[{\varpi}_{\mathcal{k}}\right]}_{\mathcal{K}}\right)\) (Table 4), which was subsequently used in the following stages of the proposed hybrid decision-making framework. Stage 2 (Application): Determining the weights for each criterion using FF-Entropy: Stage 2 aims to determine the relative importance of the evaluation criteria in the selection of AI-enhanced custom-made print advertisements. To accomplish this objective, seven sequential steps were performed. In Step 2–1, each AI-enhanced custom-made print advertisement was evaluated (Table S.3) by the experts (using linguistics scale Table 2) with respect to the predefined criteria, and the individual evaluation matrices \(\left({\widetilde{\mathcal{E}}}^{\left({\mathcal{D}}_{\mathcal{k}}\right)}={\left[{{\widetilde{\mathcal{E}}}^{\left({\mathcal{D}}_{\mathcal{k}}\right)}}_{\mathcal{i}\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) were constructed (Table S.4). In Step 2–2, these individual matrices were aggregated using the experts’ weight vector obtained in Stage 1. The FFWPDMSM aggregation operator (Eq. (6)) was employed\(\left(l=\text{1,2},\dots ,{o}_{t}=3\right);\)\(\left(l=2\right) ;\left(\mathcal{k}=1, 2,\dots ,c=3\right);\)\(\left(\mathcal{k}=1=\left\{{\mathcal{D}}_{1},{\mathcal{D}}_{2},{\mathcal{D}}_{6}\right\}\right);\)\(\left(\mathcal{k}=2=\left\{{\mathcal{D}}_{3},{\mathcal{D}}_{5},{\mathcal{D}}_{7}\right\}\right);\)\(\left(\mathcal{k}=3=\left\{{\mathcal{D}}_{4},{\mathcal{D}}_{8},{\mathcal{D}}_{9}\right\}\right)\) to integrate the weighted expert assessments into a single collective FF decision matrix \(\left(\widetilde{\mathcal{E}}={\left[{\widetilde{\mathcal{E}}}_{\mathcal{i}\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) (Table S.5) while preserving the interrelationships among the criteria. In Step 2–3, the aggregated FF numbers were converted (Eq. (7)) into crisp values \(\left(\mathcal{E}={\left[{\mathcal{E}}_{\mathcal{i}\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) (Table S.6). In Step 2–4, the crisp decision matrix was normalized (Eq. (8)) to transform all values into the interval [0,1] \(\left(\mathcal{F}={\left[{\mathcal{F}}_{\mathcal{i}\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) (Table S.7). In Step 2–5, the entropy values required for the FF-Entropy weighting procedure were calculated (Eq. (9)) (Table S.8). Subsequently, in Step 2–6, the differentiation values \(\left(\mathcal{H}={\left[{\mathcal{H}}_{\mathcal{j}}\right]}_{\mathcal{J}}\right)\) of the criteria were determined (Eq. (10)) (Table S.8) to measure their discriminative power. Finally, in Step 2–7, the differentiation values were standardized (Eq. (11)) to obtain the final criterion weight vector \(\left(\mathfrak{w}={\left[{\mathfrak{w}}_{\mathcal{j}}\right]}_{\mathcal{J}}\right)\) within the interval [0,1] (Table 5), representing the relative influence of each criterion on the selection of AI-enhanced custom-made print advertisements. These weights were then used as inputs to the subsequent FF-OPLO-POCOD ranking procedure. Stage 3 (Application): Establishing the rankings of alternatives through the application of the FF-OPLO-POCOD method: Stage 3 focuses on ranking the twelve AI-enhanced custom-made print advertisement alternatives by considering the criterion weights obtained in Stage 2. This stage consists of nine sequential steps. In Step 3–1, the best values \(\left(\mathcal{L}={\left[{\mathcal{L}}_{\mathcal{j}}\right]}_{\mathcal{J}}\right)\) required for implementing the FF-OPLO-POCOD method were identified (Eq. (12)) (Table S.9). In Step 3–2, the corresponding opportunity loss values \(\left(\mathcal{M}={\left[{\mathcal{M}}_{i\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) were calculated (Eq. (13)) (Table S.10). In Step 3–3, these values were transformed into (Eq. (13)) ordered pairs \(\left(\mathcal{N}={\left[{\mathcal{N}}_{i\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) to establish the basis for the POCOD analysis (Table S.11). In Step 3–4, the best ordered pair values \(\left(\mathcal{O}={\left[{\mathcal{O}}_{\mathcal{j}}\right]}_{\mathcal{J}}\right)\) were determined (Eq. (15)) (Table S.12), and in Step 3–5, the distances \(\left(\mathcal{P}={\left[{\mathcal{P}}_{i\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) between each advertisement alternative and the corresponding best ordered pair were computed (Eq. (16)) (Table S.13). In Step 3–6, these distances were weighed (Eq. (17)) \(\left(\mathcal{Q}={\left[{\mathcal{Q}}_{i\mathcal{j}}\right]}_{\mathcal{I}x\mathcal{J}}\right)\) using the criterion weight vector obtained from the FF-Entropy method (Table S.14). Subsequently, in Step 3–7, the total weighted distances \(\left(\mathcal{R}={\left[{\mathcal{R}}_{i}\right]}_{\mathcal{I}}\right)\) for each advertisement alternative were calculated (Eq. (18)) (Table S.15). In Step 3–8, the degree of opportunity loss values \(\left(\mathcal{S}={\left[{\mathcal{S}}_{i}\right]}_{\mathcal{I}}\right)\) was determined for all alternatives (Eq. (19)) (Table S.15). Finally, in Step 3–9, the percentage of opportunity achievement values \(\left(\mathcal{T}={\left[{\mathcal{T}}_{i}\right]}_{\mathcal{I}}\right)\) was computed (Eq. (20)) and used to rank the AI-enhanced custom-made print advertisement alternatives (Table 6). Based on the obtained ranking results, the overall performance order of the twelve advertisement alternatives was established, with Ads-4 achieving the highest performance and being identified as the most effective AI-enhanced custom-made print advertisement. Application Phase 4: Sensitivity and Comparative Tests for Custom-Made Print Ads Selection Sensitivity Analysis The selection results of AI-enhanced custom-made print ads were obtained using the FF-Entropy-OPLO-POCOD hybrid method. To test the robustness of the results, three different sensitivity analysis scenarios (SAS) were developed. In SAS-1, each evaluation criterion for the ads produced by AI, which was part of the decision model, was removed one by one, and the algorithm was rerun. In SAS-2, the lowest-ranked ad identified in the initial study was removed from the decision model to identify the best ad, and the algorithm was rerun. This process was repeated until only the two best ads remained, after which the top ad was identified. In SAS-3, the conditions for the parameter \(l\) with potential values of \(l=1\), \(l=2\), and \(l=3\), were examined individually. The results of SAS-1 are presented in Table 7 for the rankings. Figure 4 shows the final advertisement scores. The analysis shows that the removal of the “degree of product–visual compatibility \(\left({\mathcal{C}}_{5}\right)\)” criterion changes the best-performing alternative from Ads-4 to Ads-6. This change can be attributed to the fact that Ads-4 and Ads-6 exhibit very similar overall performance scores under the original decision model. The \({\mathcal{C}}_{5}\) criterion provides a greater comparative advantage for Ads-4 than for Ads-6, allowing Ads-4 to achieve the highest overall ranking when all evaluation criteria are considered. Once this criterion is excluded, the performance difference between the two alternatives becomes negligible, enabling Ads-6 to move to the first position. Since Ads-6 is originally ranked second and its overall performance is very close to that of Ads-4, this ranking change is expected and reflects the sensitivity of the results to the discriminative influence of the degree of product–visual compatibilit criterion. In all other sensitivity analysis scenarios, the removal of individual criteria does not alter the top-ranked alternative, indicating that the proposed decision framework produces stable and robust ranking results. The results of SAS-2 are shown in Table 8. In this scenario, where the lowest-ranked ad was sequentially removed, Ads-4 emerged as the top-ranked ad across all applications. The results of SAS-3 are displayed in Fig. 5. Minor variations were observed in this scenario, particularly for parameter values \(c=3\), and \(l=3\), where Ads-9 was identified as the best ad. In all other conditions, Ads-4 was determined to be the best ad. Comparative Analysis To test the consistency of the application, results obtained from the FF-Entropy-OPLO-POCOD hybrid method, analyses were conducted by comparing it with various MCDM methods found in the literature. In this context, decision problems related to the ads designed using AI were solved using AROMAN [83], ARTASI [84], MABAC [85], MARCOS [86], SAW, and WASPAS [87] methods. The results are presented in Table 9. Figure 6 displays the final values of the ads standardized through max–min normalization. According to the results obtained, Ads-4 was identified as the best-designed ad across all methods. Furthermore, the rankings obtained from the FF-Entropy-OPLO-POCOD hybrid method align perfectly with those from the SAW and WASPAS methods. Minor ranking variations were observed when compared to the other methods. According to the ranking results obtained from the comparative analysis, the correlation analysis indicates that the proposed FF-Entropy-OPLO-POCOD method exhibits perfect (100%) rank correlation (Pearson) with the SAW and WASPAS methods. Furthermore, the proposed method demonstrates correlation coefficients exceeding 98% with all other comparison methods, indicating a high level of consistency and robustness in the ranking results. Ultimately, it can be concluded that the FF-Entropy-OPLO-POCOD hybrid method serves as a suitable DSS for the ad selection process. This hybrid method is recommended for use in ad selection due to its consistency and robustness. Compared with these alternative methods, the proposed FF-Entropy-OPLO-POCOD framework provides the following methodological advantages: - Compared with AROMAN, the method evaluates alternatives by jointly considering opportunity losses and distances from ideal reference points. - Compared with ARTASI, the method considers not only the distance from the ideal solution but also the opportunity losses associated with non-selected alternatives through its polar coordinate framework. - Compared with MABAC, the method minimizes opportunity losses based on distances to polar reference points rather than distances to the border approximation area. - Compared with MARCOS, the method ranks alternatives based on the degree of opportunity loss rather than solely on their distances from ideal and anti-ideal solutions. - Compared with SAW, the method is based on distance and opportunity-loss calculations rather than simple normalized weighted summation. - Compared with WASPAS, the method evaluates alternatives based on their distances to the best ordered pair values, rather than using weighted additive and multiplicative aggregation. Overall, while the method offers a more comprehensive and robust decision-making framework by simultaneously providing opportunity-loss-based alternative evaluation. Results and Implications Results In this paper, the FF-Entropy-OPLO-POCOD Hybrid Method was proposed as DSS for the selection of AI-enhanced custom-made print ads. The method was applied through a case study. As a result of the application, custom-made print ads were successfully designed using AI support. Subsequently, the best ads were selected from the alternatives using the FF-Entropy-OPLO-POCOD Hybrid Method. The study’s findings yielded insights into the weightings of decision-makers, the weights oh criteria, and the ranking of the ads. Three main outputs were derived from the proposed algorithm, as follows: - At the conclusion of the first stage, the weights of the experts were calculated using FF sets, with the ranking as follows: “\({\mathcal{D}}_{1}={\mathcal{D}}_{2}={\mathcal{D}}_{6}>{\mathcal{D}}_{3}={\mathcal{D}}_{5}={\mathcal{D}}_{7}>{\mathcal{D}}_{4}={\mathcal{D}}_{8}={\mathcal{D}}_{9}\)”. According to this ranking, the first, second, and sixth experts played the main roles for decision process. - In the second stage, using the FF-Entropy and FFWPDMSM aggregation operators, the criterion weights were ranked as follows: “level of ethical concerns” \(\left({\mathcal{C}}_{12}\right)\) > “level of visual appeal” \(\left({\mathcal{C}}_{1}\right)\) > “level of color incompatibility” \(\left({\mathcal{C}}_{11}\right)\) > “level of purchase desire generation” \(\left({\mathcal{C}}_{3}\right)\) > “degree of product-visual compatibility” \(\left({\mathcal{C}}_{5}\right)\) > “level of purpose reflectiveness” \(\left({\mathcal{C}}_{7}\right)\) > “level of call to action” \(\left({\mathcal{C}}_{4}\right)\) > “level of clarity/comprehensibility of image and message” \(\left({\mathcal{C}}_{8}\right)\) > “level of creativity” \(\left({\mathcal{C}}_{9}\right)\) > “level of typography suitability” \(\left({\mathcal{C}}_{10}\right)\) > “level of generating interest” \(\left({\mathcal{C}}_{2}\right)\) > “level of target audience compatibility” \(\left({\mathcal{C}}_{6}\right)\). In this case, the most important criterion was identified as the “level of ethical concerns”. This indicates that ethical considerations were paramount in the design of AI-enhanced custom-made print ads. The second most important criterion was the “level of visual appeal”, demonstrating that the visual attractiveness of the ads played a predominant role. “Level of color incompatibility” ranked third, revealing that both ethical concerns and color incompatibility, as cost-related criteria, played a crucial role in the decision process. - By the end of the third stage, the ranking of the AI-enhanced custom-made print ads was as follows: “\({\mathcal{B}}_{4}>{\mathcal{B}}_{6}>{\mathcal{B}}_{9}>\)\({\mathcal{B}}_{5}>{\mathcal{B}}_{7}>{\mathcal{B}}_{3}>{\mathcal{B}}_{8}>\)\({\mathcal{B}}_{2}>{\mathcal{B}}_{10}>{\mathcal{B}}_{1}>{\mathcal{B}}_{11}>{\mathcal{B}}_{12}\)”. According to this ranking, the fourth ad was deemed the most successful. Thus, the FF-Entropy-OPLO-POCOD hybrid method was successfully applied, accounting for varying expert opinions and differing ad selection criteria, and the results were obtained. The results of the SAS tests yielded the following conclusions: - When the “degree of product-visual compatibility” \(\left({\mathcal{C}}_{5}\right)\) was removed from the model, the alternative changed to Ads-6. Given that this criterion evaluates the relationship between the product and its visual representation, it can be inferred that AI-designed ads may exhibit shortcomings in the product-visual relationship, leading to variations in ad selection. - In the application of the FF-Entropy-OPLO-POCOD hybrid method, when the lowest-ranked ad was removed and the algorithm rerun, the best one remained consistent. This consistency supports the robustness of the model, confirming that Ads-4 is the best ad under all conditions. - Changes to the \(l\) parameter revealed that under the condition \(l=3\), the results varied. In this case study, \(l=2\) provided the best results, indicating that this parameter setting is most suitable. Comparison analyses were conducted to test the consistency of the method. The ranking results of the ads were obtained using the AROMAN, ARTASI, MABAC, MARCOS, SAW, and WASPAS methods for comparison analyses. The comparison results are: - When comparing the results of the FF-Entropy-OPLO-POCOD hybrid method with those of the AROMAN and MABAC methods, Ads-8 \(\left({\mathcal{B}}_{8}\right)\) and Ads-10 \(\left({\mathcal{B}}_{10}\right)\) advanced by one rank each, while Ads-3 \(\left({\mathcal{B}}_{3}\right)\) and Ads-2 \(\left({\mathcal{B}}_{2}\right)\) dropped by one rank each. - When comparing the FF-Entropy-OPLO-POCOD hybrid method with those of the ARTASI and MARCOS methods, Ads-10 \(\left({\mathcal{B}}_{10}\right)\) advanced by one rank, while Ads-2 \(\left({\mathcal{B}}_{2}\right)\) dropped by one rank. - When comparing the FF-Entropy-OPLO-POCOD hybrid method with those of the SAW and WASPAS methods, the rankings were observed to be identical. - Across all methods, Ads-4 \(\left({\mathcal{B}}_{4}\right)\) was identified as the best alternative ad, while Ads-12 \(\left({\mathcal{B}}_{12}\right)\) was identified as the worst alternative ad. Theoretical and Practical Implications This study provides several theoretical and practical implications for advertising, marketing, and decision support systems by integrating generative AI with a multi-attribute group decision-making framework. The proposed FF-Entropy-OPLO-POCOD hybrid method demonstrates that AI can contribute not only to the efficient generation of customized print advertisements but also to systematic, transparent, and reliable advertisement selection under uncertainty. From a theoretical perspective, this research extends the application of Social Cognitive Theory to AI-enhanced advertising. Rather than viewing AI solely as an automation technology, the findings suggest that AI functions as a cognitive decision-support mechanism that facilitates observational learning, continuous feedback, and adaptive decision-making. By generating multiple advertisement alternatives and providing structured evaluations of these alternatives, the proposed framework enables marketers to learn from AI-generated outputs, compare different design strategies, and refine their creative judgments. This iterative interaction between human expertise and AI assistance strengthens marketers’ self-efficacy in advertising decision-making and supports the continuous improvement of creative marketing practices. The study also contributes to the decision science literature by introducing the FF-Entropy-OPLO-POCOD hybrid method as a comprehensive MAGDM framework capable of handling uncertainty in expert judgments. The integration of FF sets, the FFWPDMSM aggregation operator, the FF-Entropy weighting method, and the FF-OPLO-POCOD ranking approach provide a structured methodology that simultaneously considers expert uncertainty, criterion importance, and alternative performance. The robustness analyses further demonstrate the stability and reliability of the proposed decision support system. From a practical perspective, the proposed framework offers valuable guidance for companies, advertising agencies, and marketing professionals seeking to incorporate AI into their creative processes. AI-assisted advertisement generation enables organizations to produce multiple customized advertisement alternatives rapidly, while the proposed decision support system facilitates the identification of the most effective design using objective and systematic evaluation procedures. This capability is particularly valuable for small and medium-sized enterprises, which often face financial and human resource constraints in developing professional advertising campaigns. By reducing design costs, supporting evidence-based decision-making, and improving the quality of advertisement selection, the proposed framework helps organizations compete more effectively in increasingly dynamic markets. The findings also suggest broader implications beyond the advertising sector. Since the proposed methodology combines AI-assisted content generation with structured group decision-making, it can be adapted to various domains requiring the evaluation of multiple design alternatives under uncertainty, such as product design, packaging development, branding, service innovation, and digital content creation. Future research may further extend this framework by incorporating different generative AI models, additional fuzzy environments, or alternative MCDM techniques to examine its applicability across diverse decision-making contexts. Overall, this study contributes to the growing body of research on AI-supported marketing by demonstrating that the combination of generative AI and structured decision-making frameworks can improve not only operational efficiency but also the cognitive quality of marketing decisions. The proposed approach establishes a foundation for developing intelligent decision support systems that enhance creativity, learning, and strategic decision-making in AI-assisted advertising. Conclusion This study developed and validated an AI-enhanced DSS for the design and selection of custom-made print ads by integrating generative AI with a MAGDM framework. The results demonstrate that generative AI can successfully produce multiple personalized advertisement alternatives from a single standardized prompt, offering organizations an efficient and scalable approach to creative advertising. At the same time, the study shows that selecting the most effective advertisement should not rely solely on AI-generated outputs. Instead, expert evaluations remain essential for assessing the quality, relevance, and persuasive potential of alternative designs. By integrating the FF-Entropy-OPLO-POCOD hybrid method into the evaluation process, the proposed framework enables organizations to systematically identify the advertisement that best satisfies multiple advertising criteria. From a theoretical perspective, the findings extend the application of Social Cognitive Theory to AI-assisted advertising by demonstrating that effective advertisement design emerges through the interaction of technological capabilities and human cognitive judgment rather than through AI alone. While generative AI facilitates observational learning by producing diverse creative alternatives based on learned patterns, expert evaluation introduces reflective judgment, experience, and contextual understanding into the final decision. This complementary process supports more informed and transparent advertising decisions, illustrating how human cognition and AI can jointly enhance creative performance. From a practical perspective, the proposed framework provides advertisers and marketing practitioners with a structured methodology for generating, evaluating, and selecting AI-generated custom-made print advertisements while reducing subjectivity in the decision-making process. The flexibility of the proposed framework also makes it applicable to different products, customer segments, and advertising formats, providing a valuable foundation for future research on AI-assisted marketing, personalized advertising, and intelligent decision support systems. Research Limitations This study has several limitations that should be considered when interpreting the findings. First, the empirical application was limited to AI-generated print advertisements for dairy products in Türkiye, which may restrict the generalizability of the proposed framework to other industries, products, and cultural contexts. Second, the evaluation process relied on expert judgments, making the results dependent on the experience and perspectives of the selected experts. Third, the quality and diversity of the generated advertisements were influenced by the capabilities of the selected generative AI platforms and the standardized prompts used in the study. Moreover, although the proposed decision-making framework provides a systematic evaluation of advertisement alternatives, it does not incorporate actual consumer responses or behavioral outcomes. Future Suggestions Future research may extend the proposed framework by examining its applicability across different industries, products, and cultural settings to enhance its generalizability. In addition, integrating consumer-based experiments would provide a more comprehensive assessment of the effectiveness of AI-generated advertisement. Further studies may also investigate the use of emerging generative AI models and alternative MCDM techniques and fuzzy sets to improve advertisement generation and selection performance. Future studies could investigate the effectiveness of the proposed framework across different cultural contexts, while examining how the interaction between AI-generated content and human judgment shapes advertising quality and decision-making outcomes. 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Pınar Aytekin: Investigation, Validation, Formal analysis, Writing—Original Draft, Review & Editing. Tuğçe Çelik: Investigation, Formal analysis, Writing—Original Draft, Review & Editing. Vladimir Simic: Project Administration, Formal analysis, Visualization, Validation, Writing—Original Draft, Review & Editing. Dragan Pamucar: Writing—Original Draft, Review & Editing. Corresponding author Ethics declarations Ethical Approval This article does not contain any studies with human participants or animals performed by any of the authors. Consent to Participate All authors read and approved the final manuscript. Consent to Publish All authors consent when it is published. Conflict of interest The authors declare that they have no conflict of interest. Additional information Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Electronic Supplementary Material Below is the link to the electronic supplementary material. Appendix: Notation and Abbreviations Appendix: Notation and Abbreviations Notations Indices and sets: | | |---|---| \(\mathcal{i}=\text{1,2},\dots ,\mathcal{I}\) | index of alternatives (custom-made print ads), | \(\mathcal{j}=\text{1,2},\dots ,\mathcal{J}\) | index of criteria, | \(\mathcal{k}=\text{1,2},\dots ,\mathcal{K}\) | index of experts, | \(t=1, 2,\dots ,c\) | index of partitions, | \(l=\text{1,2},\dots ,{o}_{t}\) | index of element in the partitions, | \(\mathcal{B}=\{{\mathcal{B}}_{1}, {\mathcal{B}}_{2}, \dots , {\mathcal{B}}_{\mathcal{i}}, \dots , {\mathcal{B}}_{\mathcal{I}}\}\) | set of alternatives (custom-made print ads), | \(\mathcal{C}=\{{\mathcal{C}}_{1}, {\mathcal{C}}_{2}, \dots , {\mathcal{C}}_{\mathcal{j}}, \dots , {\mathcal{C}}_{\mathcal{J}}\}\) | set of criteria, | \({\mathcal{C}}^{-}\subseteq \mathcal{C}\) | set of the cost criteria, | \({\mathcal{C}}^{+}\subseteq \mathcal{C}\) | set of the benefit criteria, | \(\mathcal{D}=\left\{{\mathcal{D}}_{1}, {\mathcal{D}}_{2}, \dots , {\mathcal{D}}_{\mathcal{k}}, \dots , {\mathcal{D}}_{\mathcal{K}}\right\}\) | set of experts | Parameters: | | \(\mathcal{C}\ge 2\) | number of criteria, | \(\mathcal{B}\ge 2\) | number of alternatives, | \(\mathcal{D}\ge 2\) | number of experts, | \({C}_{{o}_{t}}^{l}\) | \(l\)-tuple combination of \({o}_{t}\), | Variables: | | \(\mathfrak{s}\left({\widetilde{\mathcal{D}}}_{\mathcal{k}}\right)(\mathcal{k}\in \mathcal{D})\) | score function value of the expert \({\mathcal{D}}_{\mathcal{k}}\), | \({\delta}_{{\widetilde{\mathcal{D}}}_{\mathcal{k}}}(\mathcal{k}\in \mathcal{D})\) | the degrees of membership value (FF set) of the assessment by the expert \({\mathcal{D}}_{\mathcal{k}}\) for expertise level, | \({\beta}_{{\widetilde{\mathcal{D}}}_{\mathcal{k}}}(\mathcal{k}\in \mathcal{D})\) | the degrees of non-membership value (FF set) of the assessment by the expert \({\mathcal{D}}_{\mathcal{k}}\) for expertise level | \({\varpi}_{\mathcal{k}}(\mathcal{k}\in \mathcal{D})\) | significant level of the expert \({\mathcal{D}}_{\mathcal{k}}\), | \({{\widetilde{\mathcal{E}}}^{\left({\mathcal{D}}_{\mathcal{k}}\right)}}_{\mathcal{i}\mathcal{j}}(\mathcal{k}\in \mathcal{D},\mathcal{i}\in \mathcal{I},\mathcal{j}\in \mathcal{J})\) | FFN assessment of the alternative \({\mathcal{B}}_{\mathcal{i}}\) under the criterion \({\mathcal{C}}_{\mathcal{j}}\) provided by the expert \({\mathcal{D}}_{\mathcal{k}}\), | \({\delta}_{{{\widetilde{\mathcal{E}}}^{\left({\mathcal{D}}_{\mathcal{k}}\right)}}_{\mathcal{i}\mathcal{j}}}(\mathcal{k}\in \mathcal{D},\mathcal{i}\in \mathcal{I},\mathcal{j}\in \mathcal{J})\) | the degrees of membership value of the FFN assessment of the alternative \({\mathcal{B}}_{\mathcal{i}}\) under the criterion \({\mathcal{C}}_{\mathcal{j}}\) provided by the expert \({\mathcal{D}}_{\mathcal{k}}\), | \({\beta}_{{{\widetilde{\mathcal{E}}}^{\left({\mathcal{D}}_{\mathcal{k}}\right)}}_{\mathcal{i}\mathcal{j}}}(\mathcal{k}\in \mathcal{D},\mathcal{i}\in \mathcal{I},\mathcal{j}\in \mathcal{J})\) | the degrees of non-membership value of the FFN assessment of the alternative \({\mathcal{B}}_{\mathcal{i}}\) under the criterion \({\mathcal{C}}_{\mathcal{j}}\) provided by the expert \({\mathcal{D}}_{\mathcal{k}}\), | \({\widetilde{\mathcal{E}}}_{\mathcal{i}\mathcal{j}} \left(\mathcal{i}\in \mathcal{I},\mathcal{j}\in \mathcal{J}\right)\) | FFN aggregated assessment of the alternative \({\mathcal{B}}_{\mathcal{i}}\) under the criterion \({\mathcal{D}}_{\mathcal{k}}\) using FFWPDMSM aggregation operator, | \(\mathfrak{s}\left({\widetilde{\mathcal{E}}}_{\mathcal{i}\mathcal{j}}\right)\left(\mathcal{i}\in \mathcal{I},\mathcal{j}\in \mathcal{J}\right)\) | score function value of the alternative \({\mathcal{B}}_{\mathcal{i}}\) under the criterion \({\mathcal{D}}_{\mathcal{k}}\), | \({\mathcal{E}}_{\mathcal{i}\mathcal{j}} \left(\mathcal{i}\in \mathcal{I},\mathcal{j}\in \mathcal{J}\right)\) | numerical aggregated value of the alternative \({\mathcal{B}}_{\mathcal{i}}\) under the criterion \({\mathcal{D}}_{\mathcal{k}}\), | \({\mathcal{F}}_{\mathcal{i}\mathcal{j}} \left(\mathcal{i}\in \mathcal{I},\mathcal{j}\in \mathcal{J}\right)\) | the normalization value of the alternative \({\mathcal{B}}_{\mathcal{i}}\) under the criterion \({\mathcal{C}}_{\mathcal{j}}\), | the entropy value of the criterion \({\mathcal{C}}_{\mathcal{j}}\), | | \({\mathcal{H}}_{\mathcal{j}}\left(\mathcal{j}\in \mathcal{J}\right)\) | the degrees differentiation value of the criterion \({\mathcal{C}}_{\mathcal{j}}\), | \({\mathfrak{w}}_{\mathcal{j}}\left(\mathcal{j}\in \mathcal{J}\right)\) | final weighting of the criterion \({\mathcal{C}}_{\mathcal{j}}\), | \({\mathcal{L}}_{\mathcal{j}}\left(\mathcal{j}\in \mathcal{J}\right)\) | the best value for each action of the criterion \({\mathcal{C}}_{\mathcal{j}}\), | \({\mathcal{M}}_{i\mathcal{j}} \left(\mathcal{i}\in \mathcal{I},\mathcal{j}\in \mathcal{J}\right)\) | the opportunity loss value of the alternative \({\mathcal{B}}_{\mathcal{i}}\) under the criterion \({\mathcal{C}}_{\mathcal{j}}\), | \({\mathcal{N}}_{i\mathcal{j}} \left(\mathcal{i}\in \mathcal{I},\mathcal{j}\in \mathcal{J}\right)\) | the ordered pair values of the alternative \({\mathcal{B}}_{\mathcal{i}}\) under the criterion \({\mathcal{C}}_{\mathcal{j}}\), | \({\mathcal{O}}_{\mathcal{j}}\left(\mathcal{j}\in \mathcal{J}\right)\) | the best ordered pair values for each action of the criterion \({\mathcal{C}}_{\mathcal{j}}\), | \({\mathcal{P}}_{i\mathcal{j}}\left(\mathcal{i}\in \mathcal{I},\mathcal{j}\in \mathcal{J}\right)\) | the distance of pair values of the alternative \({\mathcal{B}}_{\mathcal{i}}\) under the criterion \({\mathcal{C}}_{\mathcal{j}}\), | \({\mathcal{Q}}_{i\mathcal{j}}\left(\mathcal{i}\in \mathcal{I},\mathcal{j}\in \mathcal{J}\right)\) | the weighted distance of pair values of the alternative \({\mathcal{B}}_{\mathcal{i}}\) under the criterion \({\mathcal{C}}_{\mathcal{j}}\), | \({\mathcal{R}}_{i}\left(\mathcal{i}\in \mathcal{I}\right)\) | the total distance values for each action of the alternative \({\mathcal{B}}_{\mathcal{i}}\), | \({\mathcal{S}}_{i}\left(\mathcal{i}\in \mathcal{I}\right)\) | the degree opportunity loss values for each action of the alternative \({\mathcal{B}}_{\mathcal{i}}\), | \({\mathcal{T}}_{i} \left(\mathcal{i}\in \mathcal{I}\right)\) | the final ranking value of the alternative \({\mathcal{B}}_{\mathcal{i}}\) for FF-Entropy-OPLO-POCOD hybrid method | Abbreviations Abbreviation | Stands for | |---|---| AI | : Artificial Intelligence | ARAS | : Additive Ratio Assessment | ARLON | : Alternative Ranking using Two-Step Logarithmic Normalization | AROMAN | : Alternative Ranking Order Method Accounting for Two-Step Normalization | ARTASI | : Alternative Ranking Technique Based On Adaptive Standardized İntervals | BWM | : Best–Worst Method | CRADIS | : Compromise Ranking of Alternatives from Distance to Ideal Solution | DSS | : Decision Support System | FFs | : Fermatean Fuzzy Sets | FFWPDMSM | : FF-Weighted Partitioned Dual Maclaurin Symmetric Mean | MABAC | : Multi-Attributive Border Approximation Area Comparison | MAGDM | : Multi-Attribute Group Decision-Making | MARCOS | : Measurement Of Alternatives And Ranking According To Compromise Solution | MCDM | : Multi-Criteria Decision-Making | OPLO | : Opportunity Losses | POCOD | : Polar Coordinate Distance | RANCOM | : Ranking Comparison | SAW | : Simple Additive Weighting | SIWEC | : Simple Weight Calculation | SPC | : Symmetry Point of Criterion | SWARA | : Step-wise Weight Assessment Ratio Analysis | VIKOR | : VIšeKriterijumska Optimizacija I Kompromisno Rešenje | WASPAS | : Weighted Aggregated Sum Product Assessment | Rights and permissions Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or 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You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/. About this article Cite this article Akagün, E., Yalçın, G.C., Kara, K. et al. A Fermatean Fuzzy Opportunity Losses-Based Polar Coordinate Distance Method for Artificial Intelligence-Enhanced Custom-Made Print Advertisements. Cogn Comput 18, 101 (2026). https://doi.org/10.1007/s12559-026-10642-2 Received: Accepted: Published: Version of record: DOI: https://doi.org/10.1007/s12559-026-10642-2