Problem Solving with Ordinal Measurement

Abstract

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.

A Hybrid Approach to Preference Learning with Interaction Terms

“…Note that a pair {w, w } of weight functions both in W R θ may yet lead to infer opposite preferences [2]. In order to infer further preferences not dependent on an arbitrary choice of the weight function in W R θ , we turn to a robust ordinal regression approach.…”

“…The idea of ordinal dominance based on a generalized additive utility function dates back to Fishburn and Lavalle[15] 2. Following Chu and Ghahramani[8] and by abuse of notation, we use symbol P to denote both a probability mass function (for discrete variables) and a probability density function (for continuous variables), to avoid confusion with the latent (utility) function f .H.…”

Committee Selection with a Weight Constraint Based on a Pairwise Dominance Relation

“…When the individuals are evaluated in this way (i.e., on an ordinal scale), arbitrarily assigning numerical values to classes (each class can be viewed as a grade in the scale) introduces a bias in the modeling [2]. For instance, if value 8 is assigned to class 1, value 4 is assigned to class 2 and value 1 to class 3, then the ensuing recruitment choice (the one maximizing the sum of the value according to the budget) is {1, 4}.…”