A WINDOWS Interactive Program for Constructing Objective Functions

Andranik Tangian
FernUniversität Hagen
Andranik.Tangian@Fern-Uni.Hagen.de

Abstract

The aim of the computert program is to facilitate constructing objective functions for decision making. It deals with quadratic and separable objective functions in n target variables.

The model is based on the observation that a preference of a particular type can be uniquely determined from a single indifference hypersurface (level hypersurface of the corresponding objective function). In turn, such an indifference hypersurface can be determined from a finite number of equivalent in preference alternatives (vectors of target variables). Therefore, to construct an objective function, it suffices to find several vectors of target variables which are equivalent in preference.

Finding equivalent vectors can be imagined as a choice of the appropriate vector from a menu. The user considers whether the vectors from the menu are better than, worse than, or equivalent to the reference vector, and points out the equivalent one. Such judgements are based on ordinal comparisons and don't require any numerical estimation of the utility of alternatives. Therefore, the construction of an objective function is realized within the ordinal approach to preferences.

Practically, the user's work with the program falls in the following steps.

1. Specify target variables by filling a dialog box.
2. Specify the vectors of target variables which are supposed to be equivalent in preference. For this purpose, the user fixes an n-dimensional reference vector and determines equivalent ``plane vectors" in the planes which go through the reference vector. It is done as drawing points in the corresponding planes (or as determining their coordinates directly by filling a dialog box).
3. Specify test alternatives as vectors of the target variables by filling a dialog box.
4. Interactively adjust the plane vectors with regard to the appearence of indifference curves fitted and ranking of test alternatives computed.

The user may apply several models to fit the objective function to the input data. The output of the program is as follows:

1. Table of ``expert vectors" with several groups of equivalent vectors.
2. Table of test alternatives with utility indexes and ranking computed.
3. Analytical expression of the objective function as a table of its coefficients and certain geometrical invariants (centers, principal axes, etc.).
4. Plane graphs of indifference curves (with expert vectors and test alternatives).