Abstract: On inverse semigroups, the fuzzy normal subsemigroup and fuzzy quotient subsemigroup are defined via some special fuzzy relation by using fuzzy congruence relation on set. Some basic properties of those fuzzy congruence relation, which are defined by fuzzy relation, were studied, fuzz y normal quoitent sub-semigroup R and fuzzy congruence relation μ_R on inverse semigroup S/ρ were obtained by fuzzy congruence relation β.

Key words: fuzzy relation, fuzzy normal subsemigroup, fuzzy qu otient subsemigroup