Interval articulation of superiority and precise elicitation of priorities

This paper develops an approach to obtaining precise (point) estimates of priorities of objects, in particular, coefficients of importance of criteria. It is assumed that the judgements regarding the preference superiority of one object over another are given in the forms of intervals, that is by indicating the lower and upper bounds. The suggested approach is suitable both in the case of consistent and inconsistent preferences. In the former case, the available intervals are processed by contracting them to the maximum degree, in the latter, by extending them to the minimum degree. The degrees of contraction or extension are regarded as the indexes of indeterminacy or inconsistency of preferences, and treated as multiple objective functions. A method of transformation of such a multicriterial problem to a sequence of several linear programming problems is suggested.