Multicriteria filtering methods based on concordance and non-discordance principles

This paper introduces multicriteria decision-aid methods for assigning alternatives to pre-defined categories and develops a unified framework for preference aggregation methods that are based on concordance and non-discordance principles. Within this framework, we propose new multicriteria classification procedures based on non-totally compensatory measures of preference and similarity. We assume that the categories are given a priori and are characterised by fictitious alternatives serving as reference points, each representing a typical element of a category, or each representing a boundary between two categories. Several assignment methods are presented, all based on a filtering process exploiting binary relations constructed following the concordance and non-discordance principles. We first consider the case of ordered categories and a filtering procedure exploiting valued preference relations is proposed for assessing the membership of alternatives in categories. Then we consider the case of non-ordered categories and filtering methods exploiting valued indifference relations are introduced. Finally, a small example is given.