Star-product, gamma-product, lambda-product operations on soft sets and their applications to decision-making problems

In 1999, Molodtsov introduced the theory of soft sets to address problems of uncertainty. Subsequent studies expanded upon this framework by introducing various soft set products and developing systematic decision-making processes aimed at identifying the optimal alternatives, demonstrating their effectiveness in handling uncertainty. In this thesis, new soft set products—namely, the soft gamma-product, soft lambda-product, and soft star-product—are introduced. The algebraic properties of these productss are evaluated in detail with respect to different types of subsets and equalities, including M-subset/equality, F-subset/equality, L-subset/equality, and J-subset/equality. Furthermore, the distributive properties of these operations over various soft set operations are investigated. Finally, in order to determine the optimal alternative in the decision-making scenario, these products were applied to real-life problem involving uncertainty, in a manner appropriate to the problem context, demonstrating their practical applicability in the decision-making process. This study aims to contribute to the soft set theory literature by providing both theoretical depth and practical foundations for decision-making applications.