CALCULATION OF THE RESULTING RANKING OF ALTERNATIVES BASED ON THE USE OF INCOMPLETE EXPERT RANKINGS

Abstract

Incomplete information is a characteristic feature of organizational systems. Incomplete data accompanies the decision-maker in all components of corporate security, namely the management of the organization, staff activities, company assets, implemented business processes, information and other resources, financial resources, used technologies, the company's reputation, etc. Nevertheless, a reasonable decision should be made. In particular, a common practical task is to rank alternatives of different nature. This is done by experts of high competence within the areas of responsibility. Naturally, there is a situation of decision-making with incomplete data, on the basis of which it is necessary to find a complete resulting ranking of alternatives, which best approximates the information obtained from experts, ie is in some sense closest to the given incomplete expert rankings. In order to compare different ways to achieve the resulting ranking of alternatives, the formalization of the problem in the classes of single-criteria and multicriteria models for the metrics of Cook, Heming, Euclid and Litvak is considered. To solve the problems that arise in a situation of incomplete information, a number of heuristics that are empirical methodological rules that help to find solutions and contribute to the definition of mathematically incorrect problems are introduced. The notion of the modified Litvak median and the Litvak compromise median, which is used using the minimax criterion, is introduced. The algorithms developed by the authors for determining the medians of expert rankings of alternatives, namely the genetic algorithm and the heuristic algorithm are described. To illustrate the results the schemes of the genetic algorithm are given. The main results of the application of the described algorithms, which illustrate the efficiency of their application to ranking problems, that are characterized by incomplete information are given.