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

Document Type: Research Paper

Authors

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.

Keywords


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