Restricted and extended theta operations of soft sets: new restricted and extended soft set operations - Sezgin Aslihan; Aybek Fi̇tnat Nur (Bulletin of Natural Sciences Research)
Since its introduction by Molodtsov in 1999, soft set theory has gained widespread recognition as a method for addressing uncertainty-related issues and modeling uncertainty. It has been used to solve several theoretical and practical issues. Since its introduction, the central idea of the theory-soft set operations-has captured the attention of scholars. Numerous limited and expanded businesses have been identified, and their attributes have been scrutinized thus far. We present a detailed analysis of the fundamental algebraic properties of our proposed restricted theta and extended theta operations, which are unique restricted and extended soft set operations. We also investigate these operations' distributions over various kinds of soft set operations. We demonstrate that, when coupled with other types of soft set operations, the extended theta operation forms numerous significant algebraic structures, such as semirings in the collection of soft sets over the universe, by taking into account the algebraic properties of the extended theta operation and its distribution rules. This theoretical subject is very important from both a theoretical and practical perspective since soft sets' operations form the foundation for numerous applications, including cryptology and decision-making procedures.