The notion of semi-generalized closed set (sg-closed set) was first introduced by Bhattacharya and Lahiri. The notion of semi-open set was introduce by N.Levine [5].The complement of a semi open set is a semi closed set. These sets were also considered by various authors and studied their properties. In 1965, L.Nachbin [4] introduced topological ordered spaces. Later some authors extended these concepts to topological ordered spaces.A topological space along with a partial order is named as a topological ordered space. Some Authors introduced and studied the notion of irresolute maps in topological spaces [9]. These types of maps can be defined on topological ordered spaces. In this paper, irresolute maps were defined on topological ordered spaces via increasing, decreasing and balanced sets. Some properties were established with examples.A topological ordered space is a triple where is a nonempty set, is a topology and is a partial order. For , define and .For a subset , define and .Then, is increasing if and decreasing if .A subset is balanced if it is both increasing and decreasing.