T-FUZZY CONGRUENCES AND T-FUZZY FILTERS OF A BL-ALGEBRA

In this note, we introduce the concept of a fuzzy filter of a BL- algebra, with respect to a t-norm briefly, T-fuzzy filters, and give some related results. In particular, we prove Representation Theorem in BL-algebras. Then we generalize the notion of a fuzzy congruence (in a BL-algebra) was defined by Lianzhen et al. to a new fuzzy congruence, specially with respect to a t- norm. We prove that there is a correspondence bijection between the set of all T-fuzzy filters of a BL-algebra and the set of all T-fuzzy congruences in that BL-algebra. Next, we show how T-fuzzy filters induce T-fuzzy congruences, and construct a new BL-algebras, called quotient BL-algebras, and give some homomorphism theorems.