Method of using the transitive graph of a Markovian process as part of ranking of heterogeneous items
Authors: Bochkov A. V. 
Published: March 2021

Hierarchy analysis developed by Thomas Saaty is a closed logical structure that uses simple and well-substantiated rules that allow solving multicriterial problems that include both quantitative, and qualitative factors, whereby the quantitative factors can differ in terms of their dimensionality. The method is based on problem decomposition and its representation as a hierarchical arrangement, which allows including into such hierarchy all the knowledge the decision-maker has regarding the problem at hand and subsequent processing of decision-makers’ judgements. As the result, the relative degree of the interaction between the elements of such hierarchy can be identified and later quantified. Hierarchy analysis includes the procedure of multiple judgement synthesis, criteria priority definition and rating of the compared alternatives. The method’s significant limitation consists in the requirement of coherence of pairwise comparison matrices for correct definition of the weights of compared alternatives. The Aim of the paper is to examine a non-conventional method of solving the problem of alternative ratings estimation based on their pairwise comparisons that arises in the process of expert preference analysis in various fields of research. Approaches are discussed to the generation of pairwise comparison matrices taking into consideration the problem of coherence of such matrices and expert competence estimation.

Method. The methods of hierarchy analysis, models and methods of the Markovian process theory were used.

Result. The paper suggested a method of using the transitive graph of a Markovian process as part of expert ranking of items of a certain parent entity subject to the competence and qualification of the experts involved in the pairwise comparison. It is proposed to use steady-state probabilities of a Markovian process as the correlation of priorities (weights) of the compared items. The paper sets forth an algorithm for constructing the final scale of comparison taking into consideration the experts’ level of competence.

Conclusion. The decision procedures, in which the experts are expected to choose the best alternatives out of the allowable set, are quite frequently used in a variety of fields for the purpose of estimation and objective priority definition, etc. The described method can be applied not only for comparing items, but also for solving more complicated problems of expert group estimation, i.e., planning and management, prediction, etc. The use of the method contributes to the objectivity of analysis, when comparing alternatives, taking into consideration various aspects of their consequences, as well as the decision-maker’s attitude to such consequences. The suggested model-based approach allows the decision-maker identifying and adjusting his/her preferences and, consequently, choosing the decisions according to such preferences, avoiding logical errors in long and complex reasoning chains. This approach can be used in group decision-making, description of the procedures that compensate a specific expert’s insufficient knowledge by using information provided by the other experts.