Properties and Arithmetic Operations of Spherical Fuzzy Sets

Abstract

After the introduction of ordinary fuzzy sets, new extensions have appeared one by one in the literature. Among these extensions, hesitant fuzzy sets are a different extension from the others with more than one membership degree for an element. Intuitionistic fuzzy sets, Pythagorean fuzzy sets, Fermatean fuzzy sets, q-rung Orthopair fuzzy sets are the members of the same class since any element in these sets is represented by a membership degree and a non-membership degree and the hesitancy depends on these degrees. Picture fuzzy sets, neutrosophic sets, and spherical fuzzy sets are the members of the same class since any element in these sets is represented by a membership degree, a non-membership degree, and a hesitancy degree assigned by independently. Spherical fuzzy sets (SFS) have been proposed by Gundogdu and Kahraman (J Intell Fuzzy Syst 36(1):337–352, 2019a). SFS should satisfy the condition that the squared sum of membership degree and non-membership degree and hesitancy degree should be equal to or less than one. In this chapter, single-valued spherical fuzzy sets and interval-valued spherical fuzzy sets are introduced with their score and accuracy functions; arithmetic and aggregation operations such as spherical fuzzy weighted arithmetic mean operator and interval-valued spherical fuzzy geometric mean operator.