Comparative analysis of PROMETHEUS methods and fuzzy relations in decision-making conditions

Abstract

The article examines the issues of researching two decision-making methods. The paper provides an algorithm for selecting various types of criteria for preference functions that give pairwise assessments of alternative values. Preference indices for all criteria are determined, and a matrix of these indices is constructed. The graph of weighted superiority is used for all alternatives based on the index matrix. Input and output flows are determined to assess the domination of alternatives. These flows ensure ranking of alternatives in complete order. Another method involves evaluating alternatives using fuzzy relations. Definitions of utility functions for given alternatives are given. Distributions of normalized assessments on an ordered scale are shown. Pairwise assessments of alternatives are considered. Decision-making for the two methods is demonstrated using the example of designing a workshop section, which is evaluated against six criteria for three alternatives. In this example, preference indices for each pair of alternatives are presented, assessments of output and input flows are provided, and a series of alternative preferences are shown. Utility functions and pairwise assessments of alternatives are presented for fuzzy relations. Assessments of the dominance share for criteria by various methods are given. The structures of criteria for methods where equivalence of values is observed and differences in the decision-making process are shown. Conclusions are drawn regarding the features that lead to discrepancies in assessments and at which stages for different methods. Recommendations are provided for using the analysis results for decision-making support. The application of the results of this research in practice will significantly enhance the efficiency of decision-making.