DOI: https://doi.org/10.15588/1607-3274-2020-2-9

THE METHOD OF ALTERNATIVE RANKING FOR A COLLECTIVE EXPERT ESTIMATION PROCEDURE

K. E. Petrov, A. O. Deineko, O. V. Chala, I. Yu. Panfоrova

Abstract


Context. The actual problem of constructing a mathematical model of a collective multi-criteria expert estimation of alternatives, which is an integral part of the automation of the intellectual decision-making process, has been solved. 

Objective. The goal of the work is to develop a method for determining relative collective multi-criteria estimation of alternatives and their subsequent ranking based on information about personal preferences of experts. The object of research is the process of analysis and decision-making in multi-criteria conditions. The subject of the research are the methods of structural and parametric identification of the model of multi-criteria estimation of alternatives.

Method. The paper proposes an approach to constructing a model of collective multi-criteria estimation of alternatives based on information about partial-order relationships established by experts on the set of available alternatives. A method for structural and parametric identification of a model of multi-criteria estimation, which based on the ideas of the theory of comparator identification is proposed. It is shown that the solution to the problem of choosing the structure of a model of optimal complexity should be carried out in the class of Kolmogorov-Gabors polynomial. To find the parameters of the estimation model, it is proposed to use a method that is based on the calculating of the Chebyshev point. It is shown that in this case, the parametric identification problem of the model can be reduced to the standard linear programming problem. The scalar collective multi-criteria estimates of alternatives obtained on the basis of the synthesized mathematical model make it possible to compare them with each other in terms of “quality” and, thus, select the “best” of them or rank them.

Results. An approach has been developed to construct a mathematical model of collective multi-criteria expert estimation, on the basis of which it is possible to determine group generalized estimates of alternatives, as well as to rank them. The results of simulation modeling, which demonstrate the practical feasibility and effectiveness of the proposed approach are presented.

Conclusions. A significant advantage of the approach is the ability to use only non-numerical information about the preferences of experts. This allows you to partially solve the problem of subjectivity of expert opinions in the process of decision-making and reduce the cost of a collective expert estimation of alternatives. The synthesized model of collective expert estimation can serve as the basis for solving the problems of estimating the quality of various projects, investment management, strategic planning, and the development of problem-oriented decision support systems. In the future, it is worth considering the possibility of supplementing the presented approach with the possibility of taking into account estimates of the qualitative composition and competence of individual experts, which are included in the group. 


Keywords


Decision making, utility theory, multi-criteria estimates, comparative identification, utility function.

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