A Benchmark Similarity Measures for Fermatean Fuzzy Sets

Faiz Muhammad Khan; Imran  Khan; Waqas Ahmad

doi:10.18778/0138-0680.2022.08

Authors

Faiz Muhammad Khan University of Swat, Department of Mathematics and Statistics, Sector-D, Kanju township, Swat, Khyber Pakhtunkhwa, Pakistan
Imran Khan University of Swat, Department of Mathematics and Statistics, Sector-D, Kanju township, Swat, Khyber Pakhtunkhwa, Pakistan
Waqas Ahmad University of Swat, Department of Mathematics and Statistics, Sector-D, Kanju township, Swat, Khyber Pakhtunkhwa, Pakistan

DOI:

https://doi.org/10.18778/0138-0680.2022.08

Keywords:

Fermatean fuzzy set, similarity measure, S-similarity measure

Abstract

In this paper, we utilized triangular conorms (S-norm). The essence of using S-norm is that the similarity order does not change using different norms. In fact, we are investigating for a new conception for calculating the similarity of two Fermatean fuzzy sets. For this purpose, utilizing an S-norm, we first present a formula for calculating the similarity of two Fermatean fuzzy values, so that they are truthful in similarity properties. Following that, we generalize a formula for calculating the similarity of the two Fermatean fuzzy sets which prove truthful in similarity conditions. Finally, various numerical examples have been presented to elaborate this method.

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