Beyond min aggregation in multicriteria decision: (ordered) weighted min, discri-min, leximin

Conjunctive aggregation based on min operation provides too crude a ranking of the possible alternatives in multiple criteria aggregation, since decisions are only compared on the basis of the worst-rated criteria, and also since the levels of importance of the different criteria or constraints are not taken into account. Various types of weighted min operations are distinguished. Two refinements of the minbased ordering (and of the Pareto ordering which corresponds to a fuzzy set inclusion) are presented and relations between them are laid bare. These refinements aim to increase the discriminating power of the min-based aggregation, yet keeping its noncompensatory nature. A relationship between the leximin ordering and ordered weighted averages (OWA) is also discussed. Lastly, ordered weighted min operations are introduced and are shown to be of interest when only most of the criteria have to be taken into account in the evaluation.

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