Aggregation of preferences in attitude scales

Abstract

The problem of decision-making when evaluating alternatives according to several quality criteria is considered. Information is used about the pairwise comparison of alternatives by criteria: how many times one alternative is preferable to the other. The criteria may have nonuniform scales. The method to form preferences matrices for representing numerical estimates of alternatives in attitude scales is proposed. The properties of the constructed relation are investigated. The algorithms for constructing the relation with the minimum distance from the preferences by criteria are developed. An algorithm for constructing an aggregated relation based on the summation of preferences by criteria is developed. Aggregate relation depends on the method of specifying the distance between the matrices of preferences. The proposed algorithms for constructing an aggregated relation can use coefficients of importance of criteria. The method can be applied in collective choice problems when assigning estimates to alternatives by experts. A comparison of the proposed algorithms with each other and with known decision-making methods is carried out. The software system of multi-criteria choice is developed. The task of choosing start-up projects for the purpose of investing by a venture fund has been solved.