Complementary Soft Binary Piecewise Symmetric Difference Operation: A Novel Soft Set Operation

Authors : Aslıhan Sezgin, Kubilay Dagtoros

Pages : 31-45

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Publication Date : 2023-12-31

Article Type : Research Paper

Abstract :Since Molodtsov first introduced soft set theory, a useful mathematical tool for solving problems related to uncertainties, many soft set operations have been described and used in decision making problems. In this study, a new soft set operation called complementary soft binary piecewise symmetric difference operation is defined, and its properties are examined in comparison with the basic algebraic properties of the symmetric difference operation. Moreover, it has been shown that the collection of soft sets with a fixed set of parameter together with complementary soft binary symmetric difference and restricted intersection, is a commutative hemiring with identity and also a Boolean ring.
Keywords : Soft sets, soft set operations, Boolean rings, hemirings