The Recalculation of the Weights of Criteria in MCDM Methods Using the Bayes Approach

The application of multiple criteria decision-making methods (MCDM) is aimed at choosing the best alternative out of the number of available versions in the absence of the apparently dominant alternative. One of the two major components of multiple criteria decision-making methods is represented by the weights of the criteria describing the considered process. The weights of the criteria quantitatively express their significance and influence on the evaluation result. The criterion weights can be subjective, i.e., based on the estimates assigned by the experts, and the so-called objective, i.e., those which assess the structure of the data array at the time of evaluation. Several groups of experts, representing the opinions of various interested parties may take part in the evaluation of criteria. The evaluation data on the criterion weights also depend on the mathematical methods used for calculations and the estimation scales. In determining the objective weights, several methods, assessing various properties or characteristics of the data array’s structure, are usually employed. Therefore, the use of the procedures, improving the accuracy of the evaluation of the weights’ values and the integration of the obtained data into a single value, is often required. The present paper offers a new approach to more accurate evaluation of the criteria weights obtained by using various methods based on the idea of the Bayes hypothesis. The performed investigation shows that the suggested method is symmetrical and does not depend on the fact whether a priori or posterior values of the weights are recalculated. This result is the theoretical basis for practical use of the method of combining the weights obtained by various approaches as the geometric mean of various estimates. The ideas suggested by the authors have been repeatedly used in the investigation for combining the objective weights, for recalculating the criteria weights after obtaining the estimates of other groups of experts and for combining the subjective and the objective weights. The recalculated values of the weights of the criteria are used in the work for evaluating the quality of the distant courses taught to the students.