New type of extended operations of soft sets: Complementary extended union, plus and theta operation

Soft set operations constitute the basic building block of soft set theory, which was introduced by Molodtsov in 1999 to model some problems involving uncertainty. In this thesis, in order to contribute to the theory, a new soft set operation form, called complementary extended operation, is defined. In this context, complementary extended union, complementary extended plus and complementary extended theta operations are defined, their examples are given, all the properties of these operations are discussed in detail, in order to obtain the relationship of each operation with other soft set operations, the distribution of these operations over other soft set operations are examined, and the algebraic structures that the complementary extended union operation form on the set of soft sets with a fixed parameter set are discussed in detail. In the first part of the thesis, which consists of six sections, a literature review is made about soft sets and the algebraic structures mentioned in the thesis, and in the second part, basic concepts about basic set operations, soft sets and some algebraic structures are included. In the third, fourth and fifth chapters, which constitute the original part of the thesis, the complementary extended union, complement extended plus and complement expanded theta operations are introduced, respectively, and all properties of the operations such as closure, union, unit element, inverse element, commutation, the idempotent property are examined, and their relationships of these operations with other operations are investigated. For this purpose, the distributions of these operations over other soft set operations are taken into consideration. The properties of the union operation, which also exists in classical set theory, and the complementary extended union operation are compared and many remarkable results are obtained. Moreover, by showing that the complementary extended union operation, along with other soft set operations, are commutative, idempotent, unitary, non-zero semiring, commutative, idempotent, unitary hemiring, Boolean Algebra, De Morgan Algebra and MV-algebra, it has also contributed to classical algebra. In the results and recommendations section, the results obtained and the importance of the results are included.