Methods of Multi-Criteria Judgment and Selection of Objects Based on Relations with the k-th Order of Strict Preference

Abstract

Methods of multi-criteria judgment and selection of objects based on the resulting relation with the к -th order of their strict preference are proposed. It is shown that the resulting Pareto and Slater dominance relations are a special case of the resulting relationship with the k-th order of strict preference. A detailed analysis of the method of narrowing the set of nondominable objects, which is based on the coefficient of relative importance (coefficient of compromise) for a pair of criteria, is carried out. Based on the example when one criterion is more important than another in advance, it is shown that there is no need to recalculate the vector estimates of objects, since the initial set of estimates narrows if one simply excludes a less important criterion from consideration. The presented methods of multi-criteria judgment and selection of objects do not require additional expert information on the importance of criteria, are mathematically justified and illustrated by an example.