Preferences aggregation based on the importance of the criteria

System analysis, control and data processing


Smerchinskaya S. O.*, Yashina N. P.*

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



Problems of multicriteria selection are some of the most widespread problem types arising while decision making. The main difficulty in conventional algorithms implementation is that they are meant for numerical estimates setting by different criteria. Moreover, the criteria scales should be uniform. Furthermore, while decision making account must be taken of the fact, that criteria may be of various importance.

The paper suggests the technique of preference aggregation by criteria and the best alternatives selection that does not require reduction of criteria scales to uniform.

The preference aggregation algorithm presented in this work with an allowance for criteria coefficients of importance is a generalization of the preference aggregation algorithm developed by the authors earlier without allowance for criteria importance. It draws on the total preference majority graph plotting. The advantage of this algorithm is that controversial paths breaking is performed by elimination of arcs of smallest weight, thus preserving and considering all expert estimates.

In the second part of the paper, the authors propose an algorithm for obtaining coefficients of the criteria importance. This technique of obtaining the coefficients is based on plotting straight lines of indifference for each pair of criteria. We plot the straight line of indifference approximating the points of indifference corresponding to vector estimation of equivalent alternatives. We obtain the equivalent alternatives through the dialogue with the decision-makers: change the values of an alternative assessment by one of the criteria, and then set the compensation on the scale of the other criteria.

This article gives examples that demonstrate the algorithm in a dialogue with decision-makers and subsequent preferences aggregation, based on the obtained weighting factors when comparing of criteria importance and the procurement of medium-range passenger aircraft.


decision-making, multi-criteria choice, preference relations, ranging, aggregate preference, majority graph, criteria importance coefficients


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