A novel fermatean fuzzy Z-number FRANK-WASPAS model for evaluating AI-powered narrative intelligence systems

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The rise in importance of narrative intelligence systems that are inspired by artificial intelligence (AI) is increasing in terms of their ability to transmit intergenerational legacies, psychological continuity, and cultural identities. This leads to even more interest in such systems. The StoryWeaver Lab is an AI-driven app that replicates an interactive living tradition in a family. The assessment environment is rather complex and logical but ambiguous, and opposition can occur. It is difficult to model such uncertainty in an accurate way. The proposed study solves this problem with the help of comparative analysis and the weighted aggregated sum product evaluation (WASPAS) methodology. It uses a new decision-making (DM) model, which relies on the Frank norm and Fermatean fuzzy Z-numbers (FFZNs). The effectiveness of the suggested methodology is measured using a multi-attribute group DM (MAGDM) approach concerning the interdependent criteria. These criteria are narrative coherence, personal connection, ethical trustworthiness, flexibility, and long-term sustainability. The conventional MAGDM methods tend to deteriorate in case of inaccurate, partial, or reliability-sensitive data. These limitations are resolved with the use of FFZNs to describe the membership and non-membership levels and the reliability that goes with them simultaneously. The Frank norm increases the aggregate behavior by letting the criteria interact freely. This includes both reinforcing and suppressing effects. The DM model is developed based on the WASPAS method in the context of the Frank norm and FFZNs. It is evaluated in terms of consistency and strength. Mathematical case analysis of a number of AI storytelling system choices demonstrates that all methods find the same best answer. Nevertheless, the suggested FFZNs-Frank model is more interpretable. It is more reliably aware of uncertainty. Less information is lost. The results prove the legitimacy and reliability of the suggested framework. They show their benefits in comparison with traditional WASPAS. This research contributes methodologically. It offers a useful decision-support system to assess the emotional intelligence of AI systems, facilitate ethical narrative telling, sustainable cultural maintenance in unpredictable DM situations, and trustworthy human-AI relationships.