Complementary Extended Gamma Operation: A New Soft Set Operation

Since its beginnings, soft set theory has shown to be a useful mathematical framework for addressing problems involving uncertainty, proving its usefulness in a variety of academic and practical disciplines. The operations of soft sets are at the very core concept of this theory. In this regard, a new kind of soft set operation known as the complementary extended gamma operation for soft sets is presented in order to improve the theory and theoretically contribute to it in this study. To shed light on the relation between the complementary extended gamma operation and other soft set operations, a thorough analysis of this operation's attributes, including its distributions across other soft set operations, has been conducted. Additionally, this paper aims to contribute to the literature on soft sets by examining the algebraic structure of soft sets from the perspective of soft set operations, which provides a thorough grasp of their use as well as an appreciation of the ways in which soft sets can be applied to both classical and nonclassical logical thought.