Since its introduction by Molodtsov in 1999, soft set theory has gained significance as an innovative approach for handling uncertainty-related issues and modeling uncertainty. It has several applications in both theoretical and real-world settings. Researchers have been interested in soft set operations, the theory's fundamental concept, since its inception. Several restricted and extended soft set operations, one of which is restricted and extended difference operation, were defined, and their characteristics were partially investigated. The present study gives a full analysis of the properties of restricted and extended difference soft set operations, particularly in comparison to the fundamental characteristics of the difference operation existing in classical set theory, as the existing studies regarding restricted and extended set operations are quite incomplete in that all the properties of the operations have been examined in depth. In this regard, this paper is a complete study of the aforesaid soft set operations. We also observe several noteworthy properties that bear analogies to the difference operation of classical set theory. Furthermore, by investigating the distributions of these operations over all other types soft set operations including the new types of soft set operations, and taking into account the algebraic properties of the operation and its distribution rules, we demonstrate that the extended difference operation, when combined with other kinds of soft set operations, forms several significant algebraic structures, such as semiring and near-semirings in the collection of soft sets over the universe, This theoretical study has considerable significance both theoretically and practically, as the fundamental concept of the soft set theory is the operations of soft sets since they serve as the foundation for numerous applications, including cryptology, as well as the decision-making processes as correctly as possible.
Authors: Aslıhan Sezgin, Hakan Kökçü, Muhammad Riaz
DOI: https://doi.org/10.4314/ijest.v17i2.
Publish Year: 2025
