The Choice of Several Best Objects with Respect to a Partial Preference Relation

摘要

In the literature on decision making, the problem of choosing a unique best object is largely considered;ordering objects according to preference is given much less attention. However, in practice, the problem of choosing several (a given numberl> 1) of best objects often arises. An example is the choice of several best investment projects among all competing bids. Moreover,it may happen that not all of the objects are comparable with respect to preference; this is typical of, e.g., multicriteria choice problems. The current stateof-the-art in the mathematical theory of the choice of l best objects is surveyed in [1]. It was demonstrated in [1] that, although the basic definitions ofl-optimal(l-maximal) and l-undominated (l-maximal) objects were introduced as early as in 1978 [2] and some important properties of these objects were found in [3],the level of development of the theory was, obviously,insufficient, and the directions of further development were outlined. In this paper, we present the main results obtained in the course of implementation of this program.