Abstract
Soft set theory, introduced by Molodtsov, is as an efficacious mathematical tool to deal with uncertainty and it has been applied to many fields both as theoretical and application aspect. Since its inception, different kinds of soft set operations are defined and used in various types. In this paper, we define a new kind of soft set operation called, complementary soft binary piecewise gamma operation and we investigate its basic algebraic properties. Moreover by examing the distribution rules, it is aimed to contribute to the soft set literature by obtaining the relationships between this new soft set operation and other types of soft set operations such as extended soft set operations, complementary extended soft set operations, soft binary piecewise operations, complementary soft binary piecewise operations and restricted soft set operations. This paper can be regarded as a theoritical study of soft set theory.
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