Characterizations of Ordered Semigroups in Terms of Anti-fuzzy Ideals

Abstract

Adopting the notion of a (k * , q)-quasi-coincidence of a fuzzy point with a fuzzy set, the idea of an (∈ , ∈ ∨(k * , q k))-antifuzzy left (right) ideal, (∈ , ∈ ∨(k * , q k))-antifuzzy ideal and (∈ , ∈ ∨(k * , q k))-antifuzzy (generalized) bi-ideal in ordered semigroups are proposed, that are the generalization of the idea of an antifuzzy left (right) ideal, antifuzzy ideal and antifuzzy (generalized) bi-ideal in ordered semigroups and a few fascinating characterizations are obtained. In this paper, we tend to focus to suggest a connection between standard generalized bi-ideals and (∈ , ∈ ∨(k * , q k))-antifuzzy generalized biideals. In addition, different classes of regular ordered semigroups are characterized by the attributes of this new idea. Finally, the (k * , k)-lower part of an (∈ , ∈ ∨(k * , q k))-antifuzzy generalized bi-ideal is outlined and a few characterizations are mentioned.