A Novel Intuitionistic Fuzzy Entropy with Comprehensive Ranking-Stability Analysis: An Entropy-Weighted IF-TOPSIS Framework
Feride Tuğrul
Source abstract
This research introduces a novel entropy metric for assessing uncertainty in intuitionistic fuzzy sets and thoroughly examines its theoretical, practical, and resilience dimensions. The essential mathematical characteristics of the suggested entropy are demonstrated; its performance across various degrees of membership, non-membership, and hesitation is analyzed through numerical and graphical methods and contrasted with established entropy metrics. The suggested entropy is employed for the objective assessment of criterion weights, along with the IF-TOPSIS approach, and evaluated on a benchmark decision issue from the existing literature. The resultant ranking is further contrasted with the ranking presented in the first study. The method’s ranking stability is evaluated by alternative and criterion elimination analyses, Spearman and Kendall rank correlations, and diverse data perturbation situations. Furthermore, in a Monte Carlo simulation of 1000 iterations, the mean Spearman and Kendall coefficients for the suggested entropy are determined to be 0.8109 and 0.7019, respectively. The results suggest that the suggested entropy effectively maintains the overall ranking framework amidst data fluctuations and has ranking stability akin to current entropy metrics. Its relevance is further assessed by the analysis of a second autonomous issue. The findings indicate that the suggested entropy is a theoretically sound and practically viable option for objective weighting in intuitionistic fuzzy multi-criteria decision-making issues.
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