Abstract
We introduce a quotient semigroup $S/\overline{\delta}$ by an interval-valued fuzzy congruence relation $\overline{\delta}$ on a semigroup S, and present Homomorphism Theorems with respect to an interval-valued fuzzy congruence relation. In this paper, we introduce an idempotent-separating interval-valued fuzzy congruence, a group interval-valued fuzzy congruence on inverse semigroup, and some of their properties on inverse semigroups. Keywords: Interval-valued fuzzy congruence, Inverse semigroup, Idempotent-separating Interval-valued fuzzy congruence, Group Interval-valued fuzzy congruence. 2010 Mathematics Subject Classification 20M18; 18A32; 08A72.
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