Abstract
In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we ob- tain 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 residu- ated lattice and will prove that fuzzy filters and fuzzy convex subalgebras of an integral commutative residuated lattice coincide.
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