(r,s,t)-spherical fuzzy sets and their applications

This thesis focuses on (r,s,t)-spherical fuzzy sets and their interval-valued and complex extensions, which represent significant generalizations within fuzzy set theory. As an extension of classical fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets, Picture fuzzy sets, q-rung orthopair fuzzy sets, and T-spherical fuzzy sets, the (r,s,t)-spherical fuzzy sets are further enriched through the redefinition of set-theoretical and arithmetic operations, and several properties related to these operations are established. The structures of interval-valued (r,s,t)-spherical fuzzy sets and complex (r,s,t)-spherical fuzzy sets are introduced, and corresponding arithmetic operations, score and accuracy functions, as well as distance measures based on Hamming, Euclidean, and Hausdorff distances are proposed. Additionally, for interval-valued (r,s,t)-spherical fuzzy numbers, two aggregation operators—namely, the interval-valued (r,s,t)-spherical fuzzy weighted arithmetic aggregation operator and the interval-valued (r,s,t)-spherical fuzzy weighted geometric aggregation operator—are defined. Theoretical properties of these operators are analyzed and supported with illustrative examples. Based on these structures, novel multi-criteria group decision-making methods are developed using the TOPSIS approach, and explanatory examples are provided to demonstrate the applicability of the proposed methods. Furthermore, comparative analyses with existing methods are carried out to evaluate the effectiveness of the proposed models.