From 1D to 3D Membership:Sphericalfuzzy Sets

Abstract

All the extensions of ordinary fuzzy sets with three dimensional membership functions such as intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), and neutrosophic fuzzy sets (NFS) aim at defining the judgments of decision makers/ experts with a more detailed description. Introduction of generalized three dimensional spherical fuzzy sets including some essential differences from the other fuzzy sets is presented in this paper. The new type of fuzzy sets is based on the spherical relations and arithmetic operations involving addition, subtraction and multiplication are presented together with their proofs. Aggregation operators, score and accuracy functions are developed. The multi-criteria decision making method TOPSIS is extended to spherical fuzzy TOPSIS and an illustrative example is presented. A comparative analysis with intuitionistic fuzzy TOPSIS is also given.