^{1}Department of Mathematics, Shahid Beheshti University, Tehran, Iran

^{2}Department of Mathematics, Bojnord University, Bojnord, Iran

Abstract

In this note, we introduce the concept of a fuzzy filter of a BLalgebra, 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 tnorm. 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.

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