Narrowing the Pareto set on the basis of fuzzy information about the ratio of ODA preferences

Abstract

A multi-criteria choice model is considered, which includes a set of possible options, a numerical vector criterion and a fuzzy binary preference relation of the decision-maker person (DPR). The task of multi-criteria selection is to choose one or more "best" options from the Pareto set, that is, to narrow this set taking into account the information about the preference ratio of the DPR. Narrowing is carried out according to the axiomatic approach. The paper considers the algorithm for narrowing the Pareto set based on an arbitrary finite set of "quanta" of fuzzy information about the preference ratio of the DPR. Accordingly, an algorithm is proposed that allows, on the basis of an arbitrary set of clear information, to construct an estimate from above for an unknown set of options to be chosen, that is, to narrow the Pareto set. The purpose of this paper is to extend this algorithm to the case of a fuzzy preference relation, where the DPR assigns different degrees of certainty to its reasoning. In the fuzzy case under consideration, the set of options to be chosen and the top estimate constructed for it are also fuzzy. In the first section of the article, the statement of the problem of multi-criteria selection is presented and the basic axioms are formulated. The second chapter is devoted to the description of the reduction of this task to the geometric problem of constructing a fuzzy double cone. In the third section, a generalization of the algorithm is given, which makes it possible to construct the generators of a fuzzy double cone. Based on these constituents, a new vector criterion is constructed, the Pareto set with respect to which is the desired narrowing of the original Pareto set. An illustrative example is considered in the fourth chapter.