All the extensions of ordinary fuzzy sets with three dimensional membership functions such as intuitionistic fuzzy sets (IFS), intuitionistic fuzzy sets of second type (IFS2), 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 (SFS) 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 fuzzy distances which have been already defined in the literature. 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. Additionally, a comparative analysis with intuitionistic fuzzy TOPSIS (IF-TOPSIS) is given.

The extensions of ordinary fuzzy sets such as intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), and neutrosophic sets (NS), whose membership functions are based on three dimensions, aim at collecting experts’ judgments more informatively and explicitly. In the literature, generalized three-dimensional spherical fuzzy sets have been developed by Kutlu Gündoğdu and Kahraman (2019), including their arithmetic operations, aggregation operators, and defuzzification operations. Spherical Fuzzy Sets (SFS) are a new extension of Intuitionistic, Pythagorean and Neutrosophic Fuzzy sets, a SFS is characterized by a membership degree, a nonmembership degree, and a hesitancy degree satisfying the condition that their squared sum is equal to or less than one. These sets provide a larger preference domain in 3D space for decision makers (DMs). In this paper, our aim is to extend classical VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method to spherical fuzzy VIKOR (SF-VIKOR) method and to show its applicability and validity through an illustrative example and to present a comparative analysis between spherical fuzzy TOPSIS (SF-TOPSIS) and SF-VIKOR. We handle a warehouse location selection problem with four alternatives and four criteria in order to demonstrate the performance of the proposed SF-VIKOR method.