Abstract

The aim of this paper is to develop the fuzzy congruence theory of general residuated lattices. We introduce the concept of (∈, ∈ ∨ qk )-fuzzy congruence relation on a residuated lattice, and the relation between (∈, ∈ ∨ qk )-fuzzy congruences and (∈, ∈ ∨ qk )-fuzzy filters is investigated. Finally, we construct a new residuated lattice which induced (∈, ∈ ∨ qk )-fuzzy congruences, the homomorphism theorem is given.

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