On distance, similarity and entropy measures of multidimensional fuzzy sets
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.
Fields of Study & Subjects
Multi-Criteria Decision Making
Fuzzy Logic and Control Systems
Fuzzy and Soft Set Theory
Publication details
- Journal / source
- Scientific Reports
- Publisher
- Springer Science and Business Media LLC
- Volume
- 16
- Issue
- 1
- Pages
- 3525–3525
- Publication date
- 10 January 2026
- Language
- EN