Multiple criteria sorting aims at assigning alternatives evaluated on several criteria to predefined ordered categories. In this paper, we consider a well known multiple criteria sorting method, Electre Tri, which involves three types of preference parameters: (1) category limits defining the frontiers between consecutive categories, (2) weights and majority level specifying which coalitions form a majority, and (3) veto thresholds characterizing discordance effects. We propose an elicitation procedure to infer category limits from assignment examples provided by multiple decision makers. The procedure computes a set of category limits and vetoes common to all decision makers, with variable weights for each decision maker. Hence, the method helps reaching a consensus among decision makers on the category limits and veto thresholds, whereas finding a consensus on weights is left aside. The inference procedure is based on mixed integer linear programming and performs well even for datasets corresponding to real-world decision problems. We provide an illustrative example of the use of the method and analyze the performance of the proposed algorithms.

International audienceThe paper focuses on portfolio selection problems which aim at selecting a subset of alternatives considering not only the performance of the alternatives evaluated on multiple criteria, but also the performance of portfolio as a whole, on which balance over alternatives on specific attributes is required by the Decision Makers (DMs). We propose a two-level method to handle such decision situation. First, at the individual level, the alternatives are evaluated by the sorting model Electre Tri which assigns alternatives to predefined ordered categories by comparing alternatives to profiles separating the categories. The DMs' preferences on alternatives are expressed by some assignment examples they can provide, which reduces the DMs' cognitive efforts. Second, at the portfolio level, the DMs' preferences express requirements on the composition of portfolio and are modeled as constraints on category size. The method proceeds through the resolution of a Mixed Integer Program (MIP) and selects a satisfactory portfolio as close as possible to the DMs' preference. The usefulness of the proposed method is illustrated by an example which integrates a sorting model with assignment examples and constraints on the portfolio definition. The method can be used widely in portfolio selection situation where the decision should be made taking into account the performances of individual alternatives and portfolio simultaneously

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

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