Abstract
In this paper, we generalize the concept of an (is an element of, is an element of boolean OR q(k))-fuzzy quasi-ideal of an ordered semigroup, using the notion of (k*, q)-quasicoincidence of an ordered fuzzy point with a fuzzy subset of the support ordered semigroup. First we define and characterize in different ways the (is an element of, is an element of boolean OR(k*, q(k)))-fuzzy quasi-ideals of an ordered semigroup. Secondly, we present some relationships between these generalized fuzzy quasi-ideals and similar generalizations of fuzzy left/right ideals or fuzzy bi-ideals (based on the (k*, q)-quasi-coincidence relation). Similarities with quasi-ideals in ordered semigroups are discussed at the end of the paper.