Soft Binary Piecewise Theta Operation: A New Operation for Soft Sets

Abstract

After being presented by Molodtsov in 1999, soft set theory became well-known as a novel strategy for resolving uncertainty-related issues and modeling uncertainty. It has several uses in both theoretical and real-world settings.  In this study, a novel soft set operation known as the "soft binary piecewise theta operation" is presented. Its fundamental algebraic properties are investigated in detail. Furthermore, the distributions of this operation over other soft set operations are examined. In addition to being a right-left system under certain circumstances, we demonstrate that the soft binary piecewise theta operation is also a commutative semigroup in the collection of soft sets over the universe. Furthermore, by taking into account the algebraic properties of the operation and its distribution rules together, we demonstrate that the collection of soft sets over the universe, along with the soft binary piecewise theta operation and some other types of soft sets, form many important algebraic structures, like semirings and nearsemirings.