A characterization of concordance relations (original) (raw)
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A characterization of concordance relations (2002, révisé juin 2003)
The notion of concordance is central to many multiple criteria techniques relying on ordinal information, e.g. outranking methods. It leads to compare alternatives by pairs on the basis of a comparison of coalitions of attributes in terms of "importance". This note proposes a characterization of the binary relations that can be obtained using such comparisons, within a general framework for conjoint measurement that allows for intransitive preferences. We show that such relations are mainly characterized by the very rough differentiation of preference differences that they induce on each attribute.
HAL (Le Centre pour la Communication Scientifique Directe), 2005
This paper studies strict preference relations on product sets induced by "ordinal aggregation methods". Such methods are interpreted here as performing paired comparisons of alternatives based on the "importance" of attributes favoring each element of the pair: alternative x will be preferred to alternative y if the attributes for which x is better than y are "more important" than the attributes for which y is better than x. Based on a general framework for conjoint measurement that allows for intransitive preferences, we propose a characterization of such preference relations. This characterization shows that the originality of these relations lies in their very crude way to distinguish various levels of "preference differences" on each attribute when compared to the preference relations usually studied in conjoint measurement. The relation between such preference relations and P. C. Fishburn's noncompensatory preferences is investigated.
On the relationship between strict and non-strict outranking relations
2013
Outranking relations such as produced by the Electre I or II or the Tactic methods are based on a concordance and non-discordance principle that leads to declaring that an alternative is "superior" to another, if the coalition of attributes supporting this proposition is "sufficiently important" (concordance condition) and if there is no attribute that "strongly rejects" it (non-discordance condition). Such a way of comparing alternatives is rather natural and does not require a detailed analysis of tradeoffs between the various attributes. However, it is well known that it may produce binary relations that do not possess any remarkable property of transitivity or completeness. The axiomatic foundations of outranking relations have recently received attention. Within a conjoint measurement framework, characterizations of reflexive concordance-discordance relations have been obtained. These relations encompass those generated by the Electre I and II methods, which are non-strict (reflexive) relations. A different characterization has been provided for strict (asymmetric) preference relations such as produced by Tactic. The goal of this paper is to analyze the relationships between reflexive and asymmetric outranking relations. Co-duality plays an essential rôle in our analysis. It allows to understand the correspondence between the previous characterizations. Making a step further, we provide a common axiomatic characterization for both types of relations. Applying the co-duality operator to concordance-discordance relations also yields a new and interesting type of preference relation that we call concordance relation with bonus. The axiomatic characterization of such relations results directly from co-duality arguments.
Ranking methods for valued preference relations
European Journal of Operational Research, 1992
In this paper we study a particular method that builds a partial ranking on the basis of a valued preference relation. This method which is used in the MCDM method PROMETHEE I, is based on "leaving" and "entering" flows. We show that this method is characterized by a system of three independent axioms. I-Introduction Suppose that a number of decision alternatives are to be compared taking into account different points of view, e.g. several criteria or the opinion of several voters. As argued in Barrett et al. (1990) and Bouyssou (1990), a common practice in such situations is to associate with each ordered pair (a, b) of alternatives, a number indicating the strength or the credibility of the proposition "a is at least as good as b", e.g. the sum of the weights of the criteria favoring a or the percentage of voters declaring that a is preferred or indifferent to b. In this paper we study a particular method allowing to build a partial ranking, i.e. a reflexive and transitive binary (crisp) relation 2 , on A given such information. Since a partial ranking is not necessarily complete, the method considered in this paper will allow two alternatives to be declared incomparable. Though this may seem strange, it must not be forgotten that the available information may be very poor or conflictual. Declaring that a and b are incomparable thus means that it seems difficult to take, at least at this stage of the study, a definite position on the comparison of a and b.
EXPLOITATION OF A ROUGH APPROXIMATION OF THE OUTRANKING RELATION IN MULTICRITERIA CHOICE AND RANKING
Given a finite set A of actions evaluated by a family of criteria, we consider a preferential information in the form of a pairwise comparison table (PCT) including pairs of actions from a subset B⊆A×A described by graded preference relations on particular criteria and a comprehensive outranking relation. Using the rough set approach to the analysis of the PCT, we obtain a rough approximation of the outranking relation by a graded dominance relation. Decision rules derived from this approximation are then applied to a set M⊆A of potential actions. As a result, we obtain a four-valued outranking relation on set M. The construction of a suitable exploitation procedure in order to obtain a recommendation for multicriteria choice and ranking is an open problem within this context. We propose an exploitation procedure that is the only one satisfying some desirable properties.
Ordinal aggregation and strict preferences for multiattributed alternatives
2002
This paper studies strict preference relations on product sets in-duced by "ordinal aggregation methods". Such methods are inter-preted here as performing paired comparisons of alternatives based on the "importance" of attributes favoring each element of the pair: alternative x will be preferred to alternative y if the attributes for which x is better than y are "more important" than the
Advances in Data Analysis and Classification, 2021
Preference data are a particular type of ranking data where some subjects (voters, judges,...) express their preferences over a set of alternatives (items). In most real life cases, some items receive the same preference by a judge, thus giving rise to a ranking with ties. An important issue involving rankings concerns the aggregation of the preferences into a “consensus”. The purpose of this paper is to investigate the consensus between rankings with ties, taking into account the importance of swapping elements belonging to the top (or to the bottom) of the ordering (position weights). By combining the structure of \tau _x$$ τ x proposed by Emond and Mason (J Multi-Criteria Decis Anal 11(1):17–28, 2002) with the class of weighted Kemeny-Snell distances, a position weighted rank correlation coefficient is proposed for comparing rankings with ties. The one-to-one correspondence between the weighted distance and the rank correlation coefficient is proved, analytically speaking, usin...
Multiple criteria decision making: Discordant preferences and problem description
Journal of Systems Science and Systems Engineering, 2007
There are many practical decision problems where decision makers' preferences may be inconsistent and contradictory. In this paper, new methods for ordering and classifying multi-attribute objects by discordant collective preferences are suggested. These methods are based on the theory of multiset metric spaces. The proposed techniques are applied to ranking companies and a competitive selection of projects, which are estimated by several experts upon multiple qualitative criteria.
Ranking Alternatives on the Basis of a Dominance Intensity Measure
2010
The additive multi-attribute utility model is widely used within MultiAttribute Utility Theory (MAUT), demanding all the information describing the decision-making situation. However, these information requirements can obviously be far too strict in many practical situations. ...