Abstract
In this paper, we first introduce and characterize (is an element of, is an element of V(k*, q(k)))-fuzzy prime subset of the ordered semigroups. Then the (k*, k)-lower part of the (is an element of, is an element of V(k*, q(k)))-fuzzy prime subset is defined and its associated properties are studied. Moreover, the intra-regularity of ordered semigroups characterizes in terms of (is an element of, is an element of V(k*, q(k)))-fuzzy prime ideals and their (k*, k)-lower parts.