New type of extended operations of soft sets: Complementary extended difference and lamda operation

In this thesis study, some new soft set operations have been defined in order to make a contribution to the soft set theory. In this regard, complementary extended difference and complementary extended lambda operations are defined and their examples are given, the whole properties of these operations are examined in detail, the distribution rules of these operations over other soft set operations are investigated, and the algebraic structures that these operations form on the set of soft sets with a fixed parameter set are examined to obtain the relationship of each operation with other soft set operations. The thesis consists of five chapters. In the first section, a literature review is conducted on soft set theory. In the second chapter, related definitions and basic concepts of soft sets and BCK-algebra are included. In the third and fourth sections, all the properties of the complementary extended difference operation and complementary extended lambda operation together with the distributions of these operations over other operations are examined, respectively. While investigating the properties of the operations, all the properties such as closure, union, unit element, inverse element, commutative and idempotent property are examined, and especially since the difference operation is also an operation in classical set theory, it is of importance to pay attention to what kind of analogies the difference operation in classical sets have with the complementary extended difference operation in soft sets is handled and very striking results are obtained. It has been observed that the complementary extended difference operation forms BCK-algebra on the set of soft sets with a fixed parameter set. The results and obtained are included in the results and recommendations section.