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In this paper, after introducing the notion of relative bi-ideals and relative quasi ideals in ordered semigroups, some important properties of these bi-ideals and quasi ideals are studied. Then relatively prime and relatively weakly semiprime bi-ideals are defined and some vital results have been proved. We also define relative regularity and relative intraregularity of an ordered semigroup and prove some results based on the connection among intra-regularity of an ordered semigroup, relative quasi and relative bi-ideals of that ordered semigroup. Finally some important results connecting relative regularity, relatively prime bi-ideals and relatively weakly semiprime bi-ideals of an ordered semigroup have also been obtained.

Relative bi-ideals and relative quasi ideals in ordered semigroups