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Intuitionistic fuzzy value similarity measures for intuitionistic fuzzy sets

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Abstract

A new approach for defining similarity measures for intuitionistic Fuzzy (IF) sets is introduced in this paper incorporating both similarity and non-similarity measures, which called IF value similarity measures. To develop this new IF value similarity measure, the concept of IF equivalence is introduced from IF residual implicators. Methods are proposed to define the IF equivalence using IF negations, IF t-norms, and t-conorms. Then, a set of axioms is proposed and a family of IF value similarity measures is thus constructed by aggregating the IF equivalences. In the end, examples of pattern recognition are used to demonstrate the effectiveness of the proposed IF value similarity measures.

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Acknowledgements

The authors are very grateful to the editor and the anonymous referees of the journal for their excellent comments which obviously improve the manuscript.

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Authors and Affiliations

  1. School of Science, Xihua University, Chengdu, Sichuan, China

    Zichun Chen & Penghui Liu

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  1. Zichun Chen
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  2. Penghui Liu
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Correspondence to Zichun Chen.

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Communicated by Marcos Eduardo Valle.

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Chen, Z., Liu, P. Intuitionistic fuzzy value similarity measures for intuitionistic fuzzy sets. Comp. Appl. Math. 41, 45 (2022). https://doi.org/10.1007/s40314-021-01737-7

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