A Novel Distance Model and Cumulative Prospect Theory-Based Decision Analysis Under Intuitionistic Fuzzy Interval Environment

Abstract

An interval-valued intuitionistic fuzzy set enhances the classical fuzzy set by integrating both interval uncertainty and the notion of hesitation, providing a more comprehensive representation of uncertainty in decision-making situations. In various real-world scenarios, decision-makers often face complex decisions involving multiple attributes, where uncertainty prevails in the form of interval data. This paper introduces a pioneering decision analysis framework designed specifically to tackle these challenges, aiming to improve decision-making procedures’ strength and dependability (reliability) using cumulative prospect theory. We propose a novel interval-valued intuitionistic distance model to measure the distance between interval-valued intuitionistic fuzzy sets. Furthermore, we propose an extended minimax regret-based approach for comparative analysis and ranking. The effectiveness of the overall decision analysis framework is demonstrated through an illustrative example, which includes a comparison with existing distance measures. The proposed model achieves the highest degree of distinction, thereby emphasizing its enhanced discriminative capability. To further validate the model's performance, a sensitivity analysis is conducted on five key cumulative prospect theory parameters, revealing that the optimal alternative remains stable under varying parameter values, thus confirming the model's robustness. Additionally, comparative analysis with other multi-criteria decision-making approaches- MABAC, TOPSIS, VIKOR, and WASPAS- yields high Spearman rank correlation coefficients ( $\ge 0.89$ ), indicating strong consistency with established methods.