No abstract

We have shown that a variety of left(right) normal bands is closed in some homotypical varieties. Further, we partially generalize a result of Isbell from the class of commutative semigroups to some generalized classes of commutative semigroups by showing that dominion of such semigroups belongs to same classes.

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.