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A model for ordinally constructing additive objective functions. (English) Zbl 1065.90050

Summary: We investigate a method for constructing piecewise-linear approximations of an additive (called also separable) objective function in \(n\) target variables from a few indifference points in two-dimensional planes. It is shown that (a) the data used by the method are ordinal, simplest, and minimal; (b) the limit ordinal preference is independent of the cardinal utility scale used in intermediate computations, since the accuracy of the approximations is estimated in the Hausdorff metric on the space of binary relations.
The method is illustrated with an example of constructing an additive objective function of German economic policy in four target variables: Inflation, Unemployment, GNP Growth, and Increase in Public Debt. We provide some modifications of the model aimed at user’s convenience.

MSC:

90B50 Management decision making, including multiple objectives
90C29 Multi-objective and goal programming
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