Generalization of bi-polar fuzzy soft interior ideals over semirings

In this paper, we introduce the notion of a generalized bi-polar fuzzy set whose membership degree range is [-0.5,0.5], as a generalization of a fuzzy set and a bi-polar fuzzy set, the notion of generalized bi-polar fuzzy ideal, generalized bi-polar fuzzy interior ideal of semiring, generalized bi-polar fuzzy soft ideal and generalized bi-polar fuzzy soft interior ideal over semiring and study some of their algebraic properties and the relations between them.