Abstract

     The similarity measure in this paper is verified for Pythagorean fuzzy sets (PFSs). We point out that a similar measure for two PFSs is a Pythagorean fuzzy value (PFV). To calculate the similarity measure of two PFSs, it is logical that their similarity should be vague. Therefore, we introduce for the first time, as far as we know, the similarity measures for two PVFs is the same as PFV. For calculating PFV of similar measure, we first present the method for calculating Pythagorean similar measure for two PFV by using T-norm and S-norm and then extend it to calculate similar measure for two PFSs. Finally, a numerical example is provided to illustrate the validity and applicability of the presented decision-making method.

Introduction

     In many multi-criteria decision making (MCDM) problems, the decision maker has to use vague (qualitative) values to decide. In the face of qualitative values, for the first time, Bellman and his associates introduced the theory of fuzzy sets (FSs) using mathematical modeling. In making decision with fuzzy sets, the decision maker considers only the degree of correctness of the option and cannot take into account the degree of incorrectness. Continuing this trend, Atanassov in [1] introduced the intuitionistic fuzzy sets (IFSs) theory which is a generalization from FSs which included both the degrees of membership and non-membership.

     Atanassov and Gargov [2] presented an interval valued IFS (IVIFS) as a generalization and an intuitionist fuzzy sets (IFS) that makes use of interval value instead of a real number.

Conclusion

     We have successfully introduced a new definition for similarity measure for Pythagorean collections, which is also a PFV. We define the similarity measure of the two PFVs with a PFV, using T-norm, and S-norm and we generalized it to PFS. This method is used for decision making with Pythagoras value, using similarity measure. The advantages of this method include:

     Calculating the similarity size in the form of PFSs takes more information into decision making, and we lose a lot of information, if converted to a real number.