We investigate linear inequations with 5-digit of regular elements of ordered ternary semigroups, define the notions of ordered weakly left ideals, ordered weakly right ideals and ordered strong bi-ideals of ordered ternary semigroups, give some characterizations of all regular elements of ordered ternary semigroups using many kinds of ordered ideals. Finally, we investigate connections among all types of linear inequations with 5-digit of regular elements of ordered ternary semigroups.
