An In-Depth Analysis of Restricted and Extended Lambda Operations for Soft Sets - Sezgin, Aslihan; Aybek, Fitnat Nur; Stojanović, Nenad (Optimality, 2024)
Since its introduction by Molodtsov in 1999, soft set theory has gained widespread recognition as a method for modeling uncertainty and handling problems involving uncertainty. It has been used in several theoretical and practical situations. Since the theory's inception, scholars have been intrigued by its central idea-soft set operations. Several extended and restricted operations were defined, and their properties were studied. We provide new restricted and extended soft set operations that we call restricted lambda and extended lambda operations and examine their basic algebraic properties in depth. The distributions of this operation over other soft-set operations are also investigated. We demonstrate that the extended lambda operation, when combined with other kinds of soft sets, forms several significant algebraic structures, such as semirings and nearsemirings in the collection of soft sets over the universe, by taking into account the algebraic properties of the operation and its distribution rules. This theoretical research is very important both theoretically and practically, as the primary idea of the theory is the operations of soft sets, as they serve as the foundation for numerous applications, including cryptology, as well as the decision-making processes.