Restricted and extended star operations for soft sets: new restricted and extended soft set operations

Abstract

Soft set theory has been well-known as a technique for tackling uncertainty-related problems and modeling uncertainty since it was proposed by Molodtsov in 1999. It has been applied to a number of theoretical and real-world problems. The core concept of the theory-soft set operations-has piqued the interest of academics ever since it was introduced. A number of restricted and extended operations have been defined, and their characteristics have been examined up to now. Our proposed restricted star and extended star operations are novel restricted and extended soft set operations, and we thoroughly analyze their fundamental algebraic properties. We also look into the distributions of this operation over other types of soft set operations. By considering the algebraic properties of the extended star operation and its distribution rules, we show that when combined with other types of soft set operations, it forms several important algebraic structures, like semirings in the collection of soft sets over the universe. Since the operations of soft sets provide the basis for many applications, such as cryptology, and decision-making processes, this theoretical study is highly significant from both a theoretical and practical standpoint.