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Intuitionistic fuzzy similarity measures based on min–max operators

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Abstract

Intuitionistic fuzzy sets, introduced by Atanassov, offer a new possibility to describe in a more adequate way many real problems. An important tool for determining the degree of similarity between two objects is represented by similarity measures. Different types of similarity measures for intuitionistic fuzzy sets were proposed and used in various applications. More existing similarity measures involve little or no the hesitancy degree in intuitionistic fuzzy sets. The capacity of a similarity measure is determined by the form of expression and the information contained therein; more information used implies a greater power to distinguish. In this paper, we propose a family of intuitionistic fuzzy similarity measures that contain the hesitancy degree in their expression. This family represents a generalization of some known measures. For particular values of parameters, various similarity measures can be obtained: some of them are known but others are new, as will be shown in sections “The proposed intuitionistic fuzzy similarity measures” and “Conclusion”. In order to evaluate the performance of these measures, our experimental study is oriented in two basic directions: one shows how much are reasonable the proposed measures, and other describes the possibilities of application in solving some real-world problems. The experiments prove that our measures give the same results as the measures used as comparison.

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Acknowledgements

The author is grateful to the referees for their valuable comments and suggestions.

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Correspondence to Ion Iancu.

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Iancu, I. Intuitionistic fuzzy similarity measures based on min–max operators. Pattern Anal Applic 22, 429–438 (2019) doi:10.1007/s10044-017-0636-5

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Keywords

  • Intuitionistic fuzzy set
  • Similarity measure
  • Pattern recognition