Problem Solving with Ordinal Measurement

Modern socio-political-economic problems often represent situations in which the traditional numerical problem models fall far short of being adequate for determining formal solutions. The basic reason for this inadequacy is the fact that the objective functions in such problems contain abstract criteria. It, therefore, is difficult, if not impossible, to determine how much one alternative in the problem is preferred to another alternative. When such information is not available in a problem, a numerical model will serve to fabricate this information and, therefore, reduce the degree of isomorphism between the problem and the problem model.

A linear program that uses a relations set as its objective function can maintain isomorphism. In such models, the single optimal solution may not be determinable. However, if the set of feasible solutions is ordered, the optimal solution can be determined. The same ordered approach also has some useful applications to games.