Fuzzy Congruences on Semigroups

In this chapter, we introduce the notion of a fuzzy congruence relation μ on a group and a semigroup S, and a factor semigroup S/μ induced by the congruence μ. Moreover, we give homomorphism theorems for fuzzy semigroups. Finally, we consider some congruences, for example, an idempotent-separating fuzzy congruence, a group fuzzy congruence on an inverse semigroup, and a fuzzy Rees congruence.