The concept of ideal theory plays a vital role in algebraic structures. A partially ordered ternary semigroup is an algebraic structure under the ternary operator and
a partial order satisfying compatible laws. This algebraic structure is generalizations of
ordered semigroups and ternary semigroups. In this paper, we focus on studying the ideal
theory of partially ordered ternary semigroups. We define ordered almost ideals and fuzzy
ordered almost ideals in partially ordered ternary semigroups and we study some of their
properties. We give relationships between fuzzy ordered almost ideals and ordered almost
ideals of ordered semigroups.