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

A thorough mathematical foundation for dealing with uncertainty is provided by the notion of soft sets introduced by Molodtsov in 1999. In contrast to classical set theory, soft sets allow elements to have parametrization, providing a more complex representation of uncertainty. Soft set operations are important concepts in soft set theory, as they provide new approaches to dealing with problems involving parametric data. In this paper, we introduce a new soft set operation which we call “complementary extended theta operation,” to contribute to the existing theory. We thoroughly analyze the properties of the operation and investigate the relationship between the complementary extended theta operation and other soft set operations by obtaining the distribution laws in order to further study the algebraic structures of soft sets with respect to this new operation in the future studies. Since studying the algebraic structure of soft sets from the perspective of soft set operations provides a thorough understanding of their application as well as an appreciation of how soft sets can be applied to classical and non-classical logic, this paper also aims to contribute to the literature of soft sets in this regard.