New restricted and extended soft set operations

In this thesis study, by defining new soft set operations, it is aimed to make a contribution to the soft set literature. In this regard, many new soft set operations are defined, their examples are given, the whole algebraic properties of these operations are examined in detail and in order to obtain the relationship of these operations with other previously defined soft set operations and in order to see which algebraic structures these operations form on the set of soft sets over the universe U, the distribution rules of these operations over other operations have been examined. The thesis consists of seven chapters. In the first section, by investigating the previous studies in the field of soft sets, soft set operations and some algebraic structures, a literature review is conducted. The second section, which basic concepts are given, consists of three subsections. In the first subsection, the definitions and properties related to sets, in the second subsection the basic concepts as regards some algebraic structures, and in the third subsection, the basic notions related to soft sets and soft set operations are given. In the third section, the whole algebraic properties and the distributions of the restricted and extended plus operation, in the fourth section the restricted and extended gamma operation, in the fifth section the restricted and extended lambda operation, in the sixth section, the restricted and extended star operation, in the seventh section, the restricted and extended theta operation over other soft set operations are examined, and it is observed that the soft sets along with these operations form a wide variety of unary and binary algebraic structures under certain conditions such as monoid, semiring and semi near-ring. In the last section, the results obtained in the study are given in detail and the importance of the study is discussed.