Fuzzy subset Fuzzy set Green's relations Filter Decomposition of ordered semigroups Congruence Semilattice congruence Complete semilattice congruence Right ideal Left ideal Ideal Left simple Right simple Simple ordered semigroup Fuzzy right ideal Fuzzy left ideal Fuzzy ideal Fuzzy subgroupoid Fuzzy subsemigroup Fuzzy filter Fuzzy subset containing an element x Fuzzy right ideal Fuzzy left ideal Fuzzy ideal Fuzzy filter of S generated by an element x