An interval extension of the outranking approach and its application to multiple-criteria ordinal classification

Abstract

This paper presents a new outranking method whose main feature is its capacity to handle imperfect knowledge. This research is interested in two important sources of imperfect knowledge: 1) poorly known model parameters, and 2) imperfectly known (even missing) criterion values characterizing the actions. The use of interval numbers to model imperfect knowledge is suggested, and a new interval-based outranking method is proposed as an extension of the outranking approach to the interval framework. This method handles different sources of imperfect knowledge coming from model parameters (weights, veto thresholds, majority threshold) and from ill-determined, imprecise, uncertain, arbitrary (even missing) criterion values. The index of likelihood of the interval outranking is interpreted from a logical perspective, and could be used for choice, ranking and ordinal classification. Specifically, this paper proposes the method INTERCLASS for ordinal classification, which is inspired by ELECTRE TRI-B. Their assignment rules and structural properties are similar, but INTERCLASS is able to handle imprecisions in weights, veto thresholds, cutting level, and even in criteria defining limiting profiles.