Abstract
In this paper, first, we prove that the set of all fuzzy congruences on a regular semigroup contained in δ H forms a modular lattice, where δ H is the characteristic function of H and H is the H -equivalent relation on the semigroup. Secondly, we introduce idempotent separating fuzzy congruence on a semigroup and prove that the idempotent separating fuzzy congruences on a regular semigroup form a modular lattice. Finally, we prove that the lattice of fuzzy congruences on a regular semigroup is a disjoint union of some modular sublattices of the lattice.
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