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Distance measures on intuitionistic fuzzy sets based on intuitionistic fuzzy dissimilarity functions

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Abstract

One of the significant topics in intuitionistic fuzzy set (IFS) is the measure of the distance between IFSs. Although distance measures on IFSs have been widely studied in previous studies, there are few studies about the generation of them. In this paper, a quaternary function called intuitionistic fuzzy dissimilarity function is proposed to construct distance measures on IFSs. Two methods for building intuitionistic fuzzy dissimilarity functions are presented. The first one is obtained by combining dissimilarity functions and fuzzy equivalencies. The second one is obtained based on constructing new intuitionistic fuzzy dissimilarity functions through other existing ones. We also examine and compare some properties of intuitionistic fuzzy dissimilarity functions, through which we obtain some properties of distance measures on IFSs. Some examples of pattern recognition are applied to illustrate the effectiveness of the proposed distance measures on IFSs.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant Nos. 61603307 and 61473239), the Fundamental Research Funds for the Central Universities (Grant Nos. JBK170134 and JBK150503) and the Grant from MOE (Ministry of Education in China) Project of Humanities and Social Sciences (Grant No. 19YJCZH048).

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Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, Sichuan, People’s Republic of China

    Xingxing He & Keyun Qin

  2. School of Economics Information Engineering, Southwestern University of Finance and Economics, Chengdu, 611130, Sichuan, People’s Republic of China

    Yingfang Li & Dan Meng

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  1. Xingxing He
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  2. Yingfang Li
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  3. Keyun Qin
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  4. Dan Meng
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Correspondence to Yingfang Li.

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He, X., Li, Y., Qin, K. et al. Distance measures on intuitionistic fuzzy sets based on intuitionistic fuzzy dissimilarity functions. Soft Comput 24, 523–541 (2020). https://doi.org/10.1007/s00500-019-03932-5

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