SEMILATTICE CONGRUENCE AND FUZZY SEMILATTICE CONGRUENCE ON PO-Γ-SEMIGROUP VIA ITS OPERATOR SEMIGROUPS

Abstract

 In this paper, semilattice congruence and fuzzy semilattice congru
ence on po-Γ-semigroup are studied via operator semigroups. Among
 other results we obtain a lattice isomorphism between fuzzy semilattice
 congruences of a Γ-semigroup and that of its left operator semigroup.
 Using this result we have shown that any sublattice of the lattice of all
 fuzzy semilattice congruences of a po-Γ-semigroup is modular.