Analysis of decision maker's preferences structure with standard aggregative functions

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... This vector c defines the desired 2 point at n-dimensional space of indicators. This point corresponds to the radius vector, whose angles of inclination to the coordinate axes reflect the weight coefficients of the generalizing function [2]. ...
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In the paper, an approach for estimation of objects relative to specified target that was proposed by Wierzbicki A. P. is analyzed. It is asserted that this approach does not contradict with using utility (value) functions and weight coefficients at generalizing function for solving the same task. This assertion is justified by a mutual inverse relationship between functions estimating the goal achievement and deviation from a goal. It is shown that the deviation functions additionally allow solving such problems as ordering objects by penalties and bonuses, as well as by deviation from the norm. Using a simple medical example, the results of ranking patients by deviation from the norm, obtained by the criterion of minimax optimization and the additive generalizing function, are compared with equal and different values of the weighting coefficients of the indicators.
In the article, the method of staged clarification of a choice model depending on decision maker’ (DM) preferences is proposed. The method consists of several stages. At the first stage, the DM specifies an alternative that is best by its opinion. This information is used to detect a set of criteria defining the Pareto set that includes the specified alternative. At the next stage, the DM clarifies one-dimensional utility functions that have automatically been created for criteria, specifying the risk propensity or aversion. Basing on this information, the generalizing function and weight vector are selecting in order to the specified by DM alternative will be first in the resulting rating. At the last stage, if there is information about preferences on a set of alternatives, the one-dimensional utility functions are parametrized in the way that object ranks be in concordance with the specified preferences.
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