Characterizations of Ordered Semigroups in Terms of Anti-fuzzy Ideals

Adopting the notion of a (k*, q)-quasi-coincidence of a fuzzy point with a fuzzy set, the idea of an (is an element of,is an element of boolean OR(k*, q(k)))-antifuzzy left (right) ideal,(is an element of,is an element of boolean OR(k*, q(k)))-antifuzzy ideal and (.,..(k*, qk))-antifuzzy (generalized) bi-ideal in ordered semigroups are proposed, that are the generalization of the idea of an antifuzzy left (right) ideal, anti-fuzzy 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 (is an element of,is an element of boolean OR(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 (is an element of,is an element of boolean OR(k*, q(k)))-antifuzzy generalized bi-ideal is outlined and a few characterizations are mentioned.