A New Type of Extended Soft Set Operations: Complementary Extended Difference Operation

Soft set theory has many theoretical and practical applications. It was first introduced by Molodtsov in 1999 as a way to represent specific situations including uncertainty. The fundamental building blocks of soft set theory are soft set operations. Since its debut, several types of soft set operations have been defined and utilized in diverse contexts. In order to further the theory, a new soft set operation known as the complementary extended difference operation is defined in this paper. Its properties are thoroughly discussed, with particular attention to how it differs from the difference operation in classical sets. Additionally, the distribution of this operation over other types of soft set operations is examined in order to determine how this operation relates to other soft set operations.