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

Abstract

Soft set theory, pioneered by Molodtsov in 1999, presents a soft framework for managing uncertainty in data analysis and decision-making. In contrast to conventional set theory, soft sets permit elements to possess parametrization, offering a more intricate portrayal of uncertainty. In this paper, we introduce a novel type of soft set operation known as complementary extended theta soft set operations to contribute the existing theory. We thoroughly analyze the properties of this operation and investigate the relationship between the complementary extended theta operation and other soft set operations in order to further study of algebraic structures of soft sets with respect to the new operation in the future studies.