More General Forms of $(alpha, beta )$-fuzzy Ideals of Ordered Semigroups

Abstract

This paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  properties are investigated. Thecharacterization of regular ordered semigroups  in terms of$(in_{gamma},ivq)$-fuzzy left (right) ideals,$(in_{gamma},ivq)$-fuzzy bi-ideals and$(in_{gamma},ivq)$-fuzzy interior ideals is also investigated.