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Distance and similarity measures for Pythagorean fuzzy sets

  • Paul Augustine EjegwaEmail author
Original Paper
  • 34 Downloads

Abstract

The concept of Pythagorean fuzzy sets is very much applicable in decision science because of its unique nature of indeterminacy. The main feature of Pythagorean fuzzy sets is that it is characterized by three parameters, namely, membership degree, non-membership degree, and indeterminate degree, in such a way that the sum of the square of each of the parameters is one. In this paper, we present axiomatic definitions of distance and similarity measures for Pythagorean fuzzy sets, taking into account the three parameters that describe the sets. Some distance and similarity measures in intuitionistic fuzzy sets, viz, Hamming, Euclidean, normalized Hamming, and normalized Euclidean distances, and similarities are extended to Pythagorean fuzzy set setting. However, it is discovered that Hamming and Euclidean distances and similarities fail the metric conditions in Pythagorean fuzzy set setting whenever the elements of the two Pythagorean fuzzy sets, whose distance and similarity are to be measured, are not equal. Finally, numerical examples are provided to illustrate the validity and applicability of the measures. These measures are suggestible to be resourceful in multicriteria decision-making problems (MCDMP) and multiattribute decision-making problems (MADMP), respectively.

Keywords

Distance measure Fuzzy set Intuitionistic fuzzy set Similarity measure Pythagorean fuzzy set 

Notes

Acknowledgements

The author is thankful to the Editors-in-Chief: Professor Witold Pedrycz and Professor Shyi-Ming Chen for their technical comments, and to the anonymous reviewers for their suggestions, which have improved the quality of this paper.

Compliance with ethical standards

Conflict of interest

The author declares that there is no conflict of interest toward the publication of this manuscript.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics/Statistics/Computer ScienceUniversity of AgricultureMakurdiNigeria

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