A new decomposition of fuzzy continuity

In this paper, we introduce and study the notion of fuzzy b-I-open sets, which is properly placed between fuzzy openness and fuzzy b-openness regardless the fuzzy topological ideal. We deduce some characterization theorems for such concepts exactly analogous to general topology. And we define the notion of fuzzy b-I-continuous function via fuzzy b-I-open sets and some of its properties are investigated. Moreover, we give a decomposition of fuzzy continuity by using fuzzy b-I-continuous function.