On Fuzzy Bipolar Soft Ordered Semigroups

Abstract

In this paper, the concept of fuzzy bipolar soft set initiated by Naz and Shabir [22] is modified and strengthened. Consequently, the basic operations on fuzzy bipolar soft sets are redefined and their algebraic properties are studied. The notion of fuzzy bipolar soft ordered semigroup is defined and, furthermore, the concepts of fuzzy bipolar soft left (resp., right, two-sided) ideals over ordered semigroups are introduced and characterized.