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

References

[1] M. Bakhshi and R. A. Borzooei, Lattice structure of fuzzy congruence relations on a hypergroupoid,
Inform. Sci., 177(16) (2007), 3305-3316.
[2] M. Bakhshi, M. Mashinchi and R. A. Borzooei, Representation of fuzzy structures, International
Review of Fuzzy Mathematics, 1(1) (2006), 73-87.
[3] C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc., 88 (1958),
467-490.
[4] P. H´ajek, Metamathematics of fuzzy logic, Klower Academic Publishers, Dordrecht, 1998.
[5] E. P. Klement and R. Mesiar, Logical, algebraic, analytic and probabilistic aspects of triangular
norms, Elsevier, Netherlands, 2005.
[6] L. Liu and K. Li, Fuzzy filters of BL-algebras, Inform. Sci., 173 (2005), 141-154.
[7] L. Liu and K. Li, Fuzzy Boolean and positive implicative filters of BL-algebras, Fuzzy Sets
and Systems, 152 (2005), 333-348.
[8] V. Murali, Fuzzy congruence relations, Fuzzy Sets and Systems., 29 (1984), 391-394.
[9] E. Turunen, BL-algebras and basic fuzzy logic, Mathware and Soft Computing, 6 (1999),
49-61.
[10] E. Turunen, Boolean deductive systems of BL-algebras, Arch. Math. Logic, 40 (2001), 467-
473.
Iranian Journal of Fuzzy Systems
Volume 6, Issue 4 - Serial Number 4
November and December 2009
Pages 37-47

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