A novel approach on Spherical Neutrosophic Hesitant Fuzzy Sets (SNHFS)

Abstract

This paper introduces Spherical Neutrosophic Hesitant Fuzzy Sets (SNHFS) a novel extension that combines neutrosophic logic, hesitant fuzzy sets and spherical constraints to handle uncertainty and indeterminacy in decision-making scenarios. The SNHFS framework addresses the limitations of existing fuzzy set theories by incorporating three membership functions  with hesitant values while maintaining the spherical constraint that the sum of squares of membership degrees does not exceed unity. We establish fundamental set-theoretic operations, topological properties and distance measures for SNHFS. The theoretical framework includes comprehensive proofs of idempotent laws, commutative laws, associative laws and De Morgan's laws. Additionally, we develop SNHF topological spaces and investigate continuity properties. The proposed distance measure satisfies all metric properties making it suitable for similarity assessments and clustering applications. Our findings demonstrate that SNHFS provides a more flexible and robust framework for handling complex uncertainty scenarios compared to existing approaches, with potential applications in multi-criteria decision making, pattern recognition  and artificial intelligence systems.