A Theoretical Framework for Analysing the Notion of Relative Importance of Criteria

Abstract

Multiple‐criteria decision aid almost always requires the use of weights, importance coefficients or even a hierarchy of criteria, veto thresholds, etc. These are importance parameters that are used to differentiate the role devoted to each criterion in the construction of comprehensive preferences. Many researchers have studied the problem of how to assign values to such parameters, but few of them have tried to analyse in detail what underlies the notion of importance of criteria and to give a clear formal definition of it. In this paper our purpose is to define a theoretical framework so as to analyse the notion of the importance of criteria under very general conditions. Within this framework it clearly appears that the importance of criteria is taken into account in very different ways in various aggregation procedures. This framework also allows us to shed new light on fundamental questions such as: Under what conditions is it possible to state that one criterion is more important than another? Are importance parameters of the various aggregation procedures dependent on or independent of the encoding of criteria? What are the links between the two concepts of the importance of criteria and the compensatoriness of preferences? This theoretical framework seems to us sufficiently general to ground further research in order to define theoretically valid elicitation methods for importance parameters.

ELECTRE: A comprehensive literature review on methodologies and applications

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Multiple criteria aggregation procedure for mixed evaluations

“…In the literature, some methods are proposed to establish the relative importance of the criteria w j . Regarding this issue, one can refer to Mousseau [16] and Roy and Mousseau [21]. In order to build the D distance measure, Jabeur et al [12] proposed first a set of five ''logic'' conditions (an axiomatic) in which they compared the distance between each pair of binary relations {1, 1 À1 , %, ?}.…”

Integration of ordinal and cardinal information in multi-criteria ranking with imperfect compensation

“…It should be emphasized that the meaning of weights is dependent on the way the value functions are formulated and the aggregation takes place (e.g., Roy and Mousseau, 1996). For example, when decision makers or their representatives express their views on weights, they should be informed about the way the standardisation and the aggregation carried out.…”