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A novel fermatean fuzzy Z-number FRANK-WASPAS model for evaluating AI-powered narrative intelligence systems.
Muhammad Shazib Hameed1, Barira Saba1, Sobia Zulfiqar1
1Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, 64200, Pakistan.
Scientific Reports
|June 17, 2026
Summary
This study introduces a new decision-making model using Fermatean fuzzy Z-numbers and the Frank norm to assess artificial intelligence (AI) narrative systems. The FFZNs-Frank model enhances decision support for evaluating AI
Area of Science:
- Artificial Intelligence
- Decision Science
- Computational Linguistics
Background:
- Narrative intelligence systems powered by AI are gaining importance for transmitting cultural identities and legacies.
- Assessing these complex AI systems is challenging due to ambiguous environments and data uncertainty.
- Existing multi-attribute group decision-making (MAGDM) methods struggle with unreliable or incomplete data.
Purpose of the Study:
- To develop a novel decision-making (DM) model for assessing AI narrative systems in complex, uncertain environments.
- To address limitations of traditional MAGDM methods when dealing with inaccurate or reliability-sensitive data.
- To provide a robust framework for evaluating AI systems based on criteria like narrative coherence and ethical trustworthiness.
Main Methods:
- Comparative analysis utilizing the weighted aggregated sum product evaluation (WASPAS) methodology.
- Development of a new DM model based on the Frank norm and Fermatean fuzzy Z-numbers (FFZNs).
- Evaluation using a multi-attribute group DM (MAGDM) approach with interdependent criteria: narrative coherence, personal connection, ethical trustworthiness, flexibility, and long-term sustainability.
Main Results:
- The proposed FFZNs-Frank model demonstrates superior interpretability and uncertainty awareness compared to traditional methods.
- Mathematical case analysis confirmed that the FFZNs-Frank model identifies the same optimal AI storytelling system while losing less information.
- The framework proved its legitimacy and reliability, outperforming conventional WASPAS in handling uncertainty.
Conclusions:
- The FFZNs-Frank decision-support system offers a reliable method for assessing the emotional intelligence and ethical narrative capabilities of AI.
- This research contributes a methodological advancement for trustworthy human-AI relationships and sustainable cultural maintenance.
- The study validates the effectiveness of FFZNs and the Frank norm in complex decision-making scenarios involving AI.
