Soft binary piecewise operations and their properties

This master's thesis is on soft set theory, introduced by Molodtsov in 1999 to model uncertainty. Many new soft binary piecewise operations are defined, their properties are thoroughly examined, and it is examined in full detail which algebaric structures these operations together with soft sets form in the set of soft sets over the universe U and in the set of soft sets with a fixed parameter This study, consisting of ten section, begins with the first chapter where the literature on soft sets, set operations, and algebraic structures are discussed. In the second section, fundamental definitions and theorems to be used in this thesis are provided. In the third section, soft binary piecewise intersection operation; in the fourth section, the soft binary piecewise union operation; in the fifth section, the soft binary piecewise addition operation; in the sixth section, the soft binary piecewise gamma operation; in the seventh section, the soft binary piecewise lambda operation; in the eighth section, the soft binary piecewise star operation; in the ninth section, and the soft binary piecewise theta operation are introduced, their examples are given, and all the properties of these operations are examined in detail. In order to obtain the relationships of these operations with other soft set operations, the distributions of these operations on other soft set operations such as restricted, extended and soft binary piecewise operations are explored. Considering the algebraic properties and distributive rules of the operations, it is shown that the set of soft sets together with these operations form a wide variety of algebaric structures such as monoid, bounded semi-lattice, group, semiring, hemiring, left-right system, zero-symmetric right seminearring, bounded distributive lattice, Boolean ring, Boolean algebra, De Morgan Algebra, Kleene Algebra and Stone algebra under certain conditions. In the conclusion section, the results obtained from this study are presented, and the significance of the results is discussed.