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 -distance, -similarity, and -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. © The Author(s) 2025.