Matrix Science Mathematic (MSMK)

Soft set theory, introduced by Molodtsov, is as an important mathematical tool to deal with uncertainty and it has been applied to many fields both as theoretical and application aspects. Since 1999, different kinds of soft set operations has been defined and used in various types. In this paper, we define a new kind of soft set operation called, complementary soft binary piecewise plus operation and investigate its basic algebraic properties. Moreover, by examining the distribution rules, we contribute to the soft set literature by obtaining the relationships between this new soft set operation and some other types of soft set operations such as soft restrcited, extended, soft binary piecewise, and complementary soft binary piecewise operations. As proposing new soft set operations and obtaining their algebraic properties and implementations opens up new avenues for handling parametric data challenges in terms of decision-making methods and new cryptography approaches, and analyzing the algebraic structure of soft sets from the standpoint of new soft set operations offers a thorough understanding of the algebraic structure of soft sets, this paper can be regarded as both theoretical and application study.