Theta-product, plus-product, difference-product, cartesian-product operations in soft sets and their applications to decision-making problems

In this thesis, new soft set products are introduced with the aim of contributing to the theory of soft sets, and their fundamental algebraic properties are examined in detail. Within the scope of the study, the distributive properties of the defined products over restricted, extended, and binary soft partial operations are analyzed. Furthermore, by employing a decision-making method, the applicability of these products to decision-making problems is evaluated, and several illustrative examples are provided to support the understanding of the subject. The thesis is organized into six chapters, each addressing a distinct yet interconnected aspect of soft set theory. The first chapter presents a comprehensive introduction to soft sets and their foundational concepts, with particular emphasis on an in-depth review of various soft subsets and soft equalities extensively studied in the literature. Chapter two formally introduces the soft theta-product, rigorously establishes its algebraic properties, examines its distributive rules over other soft set operations, and illustrates its practical relevance through an application to real-life decision-making problems. Chapters three, four, and five are respectively devoted to the soft plus-product, the soft difference-product, and the soft cartesian product. For each of these operations, a systematic and detailed investigation is conducted, focusing on their algebraic properties, distributive behaviors over existing soft set operations, and their applicability to decision-making frameworks. The final chapter consolidates the overall findings, provides a critical evaluation of the results obtained, and underscores the theoretical significance and potential applications of the proposed soft set products, thereby highlighting the contribution of this study to the broader development of soft set theory.