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

Abstract

This paper consider the general forms of $(alpha,beta)$-fuzzy<br />left ideals (right ideals, bi-ideals, interior ideals) of an ordered<br />semigroup, where<br />$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedge<br />q_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneq<br />in_{gamma}wedge q_{delta}$. Special attention is paid to<br />$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interior<br />ideals) and some related properties are investigated. The<br />characterization of regular ordered semigroups in terms of<br />$(in_{gamma},ivq)$-fuzzy left (right) ideals,<br />$(in_{gamma},ivq)$-fuzzy bi-ideals and<br />$(in_{gamma},ivq)$-fuzzy interior ideals is also investigated.