Characterizations of regular ordered semigroups in terms of (α, β)-fuzzy generalized bi-ideals

In this paper, the concept of an (alpha, beta)-fuzzy generalized bi-ideal in an ordered semigroup is introduced, which is a generalization of the concept of a fuzzy generalized bi-ideal in an ordered semigroup. Using this concept, some characterization theorems are provided. The upper/lower parts of an (is an element of, is an element of V q)-fuzzy generalized bi-ideal are introduced and some characterizations of regular ordered semigroups are given. Also, we consider the concept of implication-based fuzzy generalized bi-ideals in an ordered semigroup. In particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed. (C) 2011 Elsevier Inc. All rights reserved.