Selecting a Single Result from an Aggregate of Contradictory Alternatives with Use of Multiset Theory

Abstract

We consider basic approaches to decision-making using computer systems. Ambiguous results in decision-making are obtained through the use of different methods for source-data processing. In order to obtain a single result from an aggregate of such decisions, it is suggested to apply the principle of selecting the decision that is most proposed by John von Neumann to increase the reliability of computers. Based on multiset theory, we develop a mathematical model of selecting a single result from an aggregate of alternatives obtained using different methods of decision-making. In this model, a decision is selected based on computing the argument of maximizing the multiplicity functions of elements for the arithmetic sum of multisets of the obtained decisions. The peculiarities of applying this approach are considered and methods of adjusting the source data for obtaining a single result are proposed. By the example of selecting a metal for electroplating products we present the results (of the decisions taken) obtained by a group of experts using the described approach. Recommendations for improving the efficiency of the proposed approach are presented.