A COMPREHENSIVE STUDY ON SOFT BINARY PIECEWISE DIFFERENCE OPERATION

Abstract

Soft set theory, developed by Molodtsov, has been applied both theoretically and practically in many fields. It is a useful mathematical tool for handling uncertainty. Numerous variations of soft set operations, which is a crucial concept for the theory, have been described and used since its introduction. In this paper, we explore more about soft binary piecewise difference operation (defined first as “difference of soft sets”) and its whole properties are examined especially in comparison with the basic properties of difference operation in classical set theory. Several striking properties of soft binary piecewise operations are obtained as analogous to the characteristic of difference operation in classical set theory. Also, we show that the collection of all soft sets with a fixed parameter set together with the soft binary piecewise difference operation is a bounded BCK-algebra.