The set of real number with addition and multiplication operation is said as field with a notation. At set of is given two binary operations that is and, are defined as follow: for all, and. The structure is called max-plus algebra, which denote as. The main different between and that is there is no invers for all element except the zero elemen. Futhermore are introduced extended of with define and at. In set of are given balance relation, denote, and relation whereas is equivalence relation since its compatible for generate equivalence class and quosien set. Clearly, the elements of set of is equivalence classes and than for all equivalenve class are assosiated with scalar or signed scalar dan in. By using definision of, and balance relation in for design the system of. In this research are performed properties of and than are defined the symmetrized max-plus algebra.