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Updated: Jan 13, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
On distance, similarity and entropy measures of multidimensional fuzzy sets
Jomal Josen1, Sunil Jacob John2, Jobish Vallikavungal3,4
1Department of Mathematics, St. Thomas College Palai (Autonomous), Arunapuram P.O., Kottayam, Kerala, 686 574, India.
Abstract:
This article examines distance and similarity measures in multidimensional fuzzy sets, which are essential in decision-making and aggregation across various fields. It defines the axioms for multidimensional distance measures and introduces a framework for normalized distance and similarity measures within a suitable fuzzy space. The concept of complement-invariant proximity measures is also discussed. The paper further explores the relationship between distance and similarity, linking them with multidimensional entropy. It presents σ-distance, σ-similarity, and σ-entropy measures that balance values between fuzzy sets and their complements. Finally, two decision-making problems are analyzed, with a comparative study showing the proposed model's advantage over existing approaches.
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