A New Soft Set Operation: Complementary Extended Star Operation

Soft set theory has established itself as a valuable mathematical framework for tackling issues marked by uncertainty, demonstrating its applicability across a range of theoretical and practical fields since its inception. Central of this theory is the operations of soft sets. To enhance the theory and to make a theoretical contribution to the theory, a new type of soft set operation, called “complementary extended star operation” for soft set, is proposed. An exhaustive examination of the properties of this operation has been undertaken, including its distributions over other soft set operations, with the goal of clarifying the relationship between the complementary extended star operation and other soft set operations. This paper also attempts to make a contribution to the literature of soft sets in the sense that studying the algebraic structure of soft sets from the standpoint of soft set operations offers a comprehensive understanding of their application as well as an appreciation of how soft set can be applied to classical and nonclassical logic.