Applied Intelligence

, Volume 49, Issue 12, pp 4058–4096 | Cite as

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

  • Xindong PengEmail author
  • Harish Garg


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.


Pythagorean fuzzy sets Similarity measures Distance measures Pattern recognition 



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).

Compliance with Ethical Standards

Conflict of interests

The authors declare no conflict of interests regarding the publication for the paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Information Sciences and EngineeringShaoguan UniversityShaoguanChina
  2. 2.School of Mathematics, Thapar Institute of Engineering & TechnologyDeemed UniversityPatialaIndia

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