In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI. Abstract In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.

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To cite this version:Brice Mayag, Michel Grabisch, Christophe Labreuche. A characterization of the 2-additive Choquet integral through cardinal information. Fuzzy Sets and Systems, Elsevier, 2011, 184 (1) AbstractIn the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions to represent a cardinal preferential information by the Choquet integral w.r.t. a 2-additive capacity. These conditions are based on some complex cycles called cyclones.

Decision support consists in helping a decision-maker to improve his/her decisions. However, clients requesting decision support are often themselves experts and are often taken by third parties and/or the general public to be responsible for the decisions they make. This predicament raises complex challenges for decision analysts, who have to avoid infringing upon the expertise and responsibility of the decision-maker. The case of diagnosis decision support in healthcare contexts is particularly illustrative. To support clinicians in their work and minimize the risk of medical error, various decision support systems have been developed, as part of information systems that are now ubiquitous in healthcare contexts. To develop, in collaboration with the hospitals of Lyon, a diagnostic decision support system for day-today customary consultations, we propose in this paper a critical analysis of current approaches to diagnostic decision support, which mainly consist in providing them with guidelines or even full-fledged diagnosis recommendations. We highlight that the use of such decision support systems by physicians raises responsibility issues, but also that it is at odds with the needs and constraints of customary consultations. We argue that the historical choice to favor guidelines or recommendations to physicians implies a very specific vision of what it means to support physicians, and we argue that the flaws of this vision partially ex-A.

International audienceEvaluating and comparing the threats and vulnerabilities associated with territorial zones according to multiple criteria (industrial activity, population, etc.) can be a time-consuming task and often requires the participation of several stakeholders. Rather than a direct evaluation of these zones, building a risk assessment scale and using it in a formal procedure permits to automate the assessment and therefore to apply it in a repeated way and in large-scale contexts and, provided the chosen procedure and scale are accepted, to make it objective. One of the main difficulties of building such a formal evaluation procedure is to account for the multiple decision makers' preferences. The procedure used in this article, Electre Tri, uses the performances of each territorial zone on multiple criteria, together with preferential parameters from multiple decision makers, to qualitatively assess their associated risk level. We also present operational tools in order to implement such a procedure in practice, and show their use on a detailed example

In collaboration with the Civil Hospitals of Lyon, we aim to develop a "transparent" classification system for medical purposes. To do so, we need clear definitions and operational criteria to determine what is a "transparent" classification system in our context. However, the term "transparency" is often left undefined in the literature, and there is a lack of operational criteria allowing to check whether a given algorithm deserves to be called "transparent" or not. Therefore, in this paper, we propose a definition of "transparency" for classification systems in medical contexts. We also propose several operational criteria to evaluate whether a classification system can be considered "transparent". We apply these operational criteria to evaluate the "transparency" of several well-known classification systems.

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Abstract. In the context of MultiCriteria Decision Aid, we present new properties of a 2-additive bi-capacity by using a bipolar Möbius transform. We use these properties in the identification of a 2-additive bicapacity when we represent a cardinal information by a Choquet integral with respect to a 2-additive bi-capacity.