A new fuzzy entropy on Pythagorean fuzzy sets

Article type: Research Article

Authors: Thao, Nguyen Xuan^{a; *} | Smarandache, Florentin^b

Affiliations: [a] Faculty of Information Teachnology–Vietnam National University of Agriculture, Hanoi, Vietnam | [b] Mathematics Department, University of New Mexico, Gallup, NM, USA

Correspondence: [*] Corresponding author. Nguyen Xuan Thao, Faculty of Information Teachnology–Vietnam National University of Agriculture, Hanoi, Vietnam. E-mail: nxthao@vnua.edu.vn.

Abstract: Pythagorean fuzzy sets are an extension of the intuitionistic fuzzy sets, and it also overcomes the limitations of the intuitionistic fuzzy sets. The entropy of a Pythagorean fuzzy set (PFS) is a measure of uncertainty related to the PFS. In this article, we exploit the concept of probability for defining the fuzzy entropy of Pythagorean fuzzy sets as an extension of the fuzzy entropy of Intuitionistic fuzzy sets (IFSs). Compared to some previous measures, the new measure is simpler, closer to the statistical significance and it reflects better fuzzy properties. After that, we give some numerical examples to compare our proposed entropy measure to some existing entropy of Pythagorean fuzzy sets. The results on numerical examples show that the proposed entropy measures seem to be more reliable for presenting the degree of fuzziness of a PFS and/or IFS. We also proposed a COPRAS multi-criteria decision-making method with weights calculated based on the proposed new entropy measure. The illustrated numerical example shows that the calculated results according to the proposed new method are similar to the calculation results according to some other existing methods.

Keywords: Pythagorean fuzzy sets, entropy measures, COPRAS method

DOI: 10.3233/JIFS-182540

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 1, pp. 1065-1074, 2019