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Multiparametric similarity measures on Pythagorean fuzzy sets with applications to pattern recognition

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Abstract

Pythagorean fuzzy sets (PFSs), characterized by membership degrees and non-membership degrees, are a more effective and flexible way than intuitionistic fuzzy sets (IFSs) to capture indeterminacy. In this paper, some new diverse types of similarity measures, overcoming the blemishes of the existing similarity measures, for PFSs with multiple parameters are studied, along with their detailed proofs. The various desirable properties among the developed similarity measures and distance measures have also been derived. A comparison between the proposed and the existing similarity measures has been performed in terms of the division by zero problem, unsatisfied similarity axiom conditions, and counter-intuitive cases for showing their effectiveness and feasibility. The initiated similarity measures have been illustrated with case studies of pattern recognition, along with the effect of the different parameters on the ordering and classification of the patterns.

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Acknowledgements

The authors are very appreciative to the reviewers for their precious comments which enormously ameliorated the quality of this paper. Our work is sponsored by the National Natural Science Foundation of China (No. 61462019), MOE (Ministry of Education in China) Project of Humanities and Social Sciences (No. 18YJCZH054), Natural Science Foundation of Guangdong Province (No. 2018A030307033, 2018A0303130274), Social Science Foundation of Guangdong Province (No. GD18CFX06).

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Authors and Affiliations

  1. School of Information Sciences and Engineering, Shaoguan University, Shaoguan, China

    Xindong Peng

  2. School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala, 147004, Punjab, India

    Harish Garg

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  1. Xindong Peng
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  2. Harish Garg
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Correspondence to Xindong Peng.

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Peng, X., Garg, H. Multiparametric similarity measures on Pythagorean fuzzy sets with applications to pattern recognition. Appl Intell 49, 4058–4096 (2019). https://doi.org/10.1007/s10489-019-01445-0

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