  The purpose of this paper is to study the generalization of inverse
semigroups (without order). An ordered semigroup S is called an inverse ordered
semigroup if for every a 2 S, any two inverses of a are H-related. We prove
that an ordered semigroup is complete semilattice of t-simple ordered
semigroups if and only if it is completely regular and inverse. Furthermore
characterizations of inverse ordered semigroups have been characterized by
their ordered idempotents.
