Abstract: This paper touched the concept of a new system of abstract algebra .Where we relied on a set of semi order, and the stack of elements in the form of a matrix. We proved that this system is a semi-group, after providing the fuzzy system to the system, and access to the algebraic operations determine the significance of any element in the set and reliance on the location element in the set . Identify new methods to resolve the issues of transportation models in Operations Research.