FUZZY CONVEX SUBALGEBRAS OF COMMUTATIVE RESIDUATED LATTICES

Document Type : Research Paper

Authors

1 Department of Mathematics of Bam, Shahid Bahonar University of Kerman, Kerman, Iran

2 Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In this paper, we define the notions of fuzzy congruence relations
and fuzzy convex subalgebras on a commutative residuated lattice and we obtain
some related results. In particular, we will show that there exists a one
to one correspondence between the set of all fuzzy congruence relations and
the set of all fuzzy convex subalgebras on a commutative residuated lattice.
Then we study fuzzy convex subalgebras of an integral commutative residuated
lattice and will prove that fuzzy filters and fuzzy convex subalgebras of
an integral commutative residuated lattice coincide.

Keywords

References

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Iranian Journal of Fuzzy Systems
Volume 7, Issue 2 - Serial Number 2
May and June 2010
Pages 41-54

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