Abstract
In this paper, we first introduce and characterize [Formula: see text]-fuzzy prime subset of the ordered semigroups. Then the [Formula: see text]-lower part of the [Formula: see text]-fuzzy prime subset is defined and its associated properties are studied. Moreover, the intra-regularity of ordered semigroups characterizes in terms of [Formula: see text]-fuzzy prime ideals and their [Formula: see text]-lower parts.
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