A New Type of Extended Soft Set Operation: Complementary Extended Intersection Operation

Abstract

Soft set theory is seen as an effective mathematical tool in solving problems involving uncertainty, and has been applied in many theoretical and practical areas since its introduction. The basic concept of the theory is soft set operations. In this context, in this paper, a new kind of soft set operations called complementary extended soft set operation is defined in order to contribute to the theory. The properties of the operation are examined in detail together with its distributions over other soft set operations in order to obtain the relationship between complementary extended intersection operation and the others. We demonstrate that the collection of soft sets over with a fixed parameter set, along with the complementary extended intersection operation and other  certain types of soft sets, form many well-known and important algebraic structures in classical algebra, including semiring, hemiring, Boolean ring, Boolean Algebra, De Morgan Algebra, Kleene Algebra, and Stone Algebra.