A COMPREHENSION OF SOFT BINARY PIECEWISE GAMMA OPERATION: A NEW OPERATION FOR SOFT SETS

Authors : Aslıhan Sezgin, Eda Yavuz, Akın Osman Atagün

Pages : 13-40

View : 9 | Download : 5

Publication Date : 2024-09-22

Article Type : Other Papers

Abstract :Soft set theory gained popularity as a cutting-edge approach to handling uncertainty-related problems and modeling uncertainty after being introduced by Molodtsov in 1999. Numerous theoretical and practical applications have been conducting by make using of the theory. This paper presents a novel soft set operation, called the "soft binary piecewise gamma operation". Its basic algebraic characteristics are thoroughly examined. Furthermore, this operation's distributions over a number of soft set operations are investigated. We prove that given certain assumptions, the soft binary piecewise addition operation determines a commutative semigroup and a right-left system, and soft binary piecewise gamma operation, along with the some other types of soft sets, form many important algebraic structures, such as semirings and near-semirings in the collection of soft sets over the universe by considering the algebraic properties of the operation and its distribution rules together.
Keywords : Soft sets, soft set operations, conditional complements, soft binary piecewise gamma operation