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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma\)</EquationSource> </InlineEquation>-distance, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\sigma\)</EquationSource> </InlineEquation>-similarity, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sigma\)</EquationSource> </InlineEquation>-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.</p>

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On distance, similarity and entropy measures of multidimensional fuzzy sets

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月10日

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  • Jomal Josen,
  • Sunil Jacob John,
  • Jobish Vallikavungal

摘要

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 \(\sigma\) -distance, \(\sigma\) -similarity, and \(\sigma\) -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.