Characterization of Ordered Semigroups in Terms of Fuzzy Soft Ideals

In this paper, we apply the concept of fuzzy soft sets to ordered semigroup theory. The concepts of (is an element of(gamma), is an element of(gamma) Vq(delta))-fuzzy left (right) ideals, (is an element of(gamma), is an element of(gamma) Vq(delta))-fuzzy bi-ideals and (is an element of(gamma), is an element of(gamma) Vq(delta))-fuzzy quasi-ideals are introduced and some related properties are obtained. Three kinds of lattice structures of the set of all (is an element of(gamma), is an element of(gamma) Vq(delta))-fuzzy soft left (right) ideals of an ordered semigroup are derived. The characterization of left quasi-regular ordered semigroups and ordered semigroups that are left quasi-regular and intra-regular in terms of (is an element of(gamma), is an element of(gamma) Vq(delta))-fuzzy left (right) ideals, (is an element of(gamma), is an element of(gamma) Vq(delta))-fuzzy bi-ideals and (is an element of(gamma), is an element of(gamma) Vq(delta))-fuzzy quasi-ideals is discussed.