An Approach for Modelling Preferences of Multiple Decision Makers (original) (raw)
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In modeling Multi-Criteria Decision Making (MCDM) problem, we usually assume that the decision maker is able to elicitate his preferences with precision and without difficulty. However, in many situations, the expert is unable to provide his assessment with certainty or he is unwilling to quantify his preferences. To deal with such situations, a new MCDM model under uncertainty is introduced. In fact, we focus here on the problem of modeling expert opinions despite the presence of incompleteness and uncertainty in their preference assessments. Besides, our proposed solution suggests to model these preferences qualitatively rather than exact numbers. Therefore, we propose to incorporate belief preference relations into a MCDM method. The expert assessments are then formulated as a belief function problem since this theory is considered as a useful tool to model expert judgments.
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Modelling the preferences of a decision maker about alternatives having multiple criteria usually starts by collecting preference information (comparisons of alternatives, importance of criteria,. . .), which are then used to fit a preference model issued from some set of hypothesis (weighted average, CP-net, lexicographic orderings,. . .). In practice, this process may often lead to inconsistencies that may be due to inaccurate information provided by the decision maker, who can be unsure about the provided information, or to a poor choice of hypothesis set, which can be too restrictive or not well adapted to the decision process. In this paper, we propose to use belief functions as a way to quantify and resolve such inconsistencies, notably by allowing the decision maker to express her/his certainty about the provided preferential information. Our framework is generic, in the sense that it does not assume a given set of hypothesis a priori, and is consistent with precise methods, in the sense that in the absence of uncertainty and inconsistencies in the information, precise models are ultimately retrieved.
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Many organizations face such complex and important management problems that they sometimes want their decisions to be somehow supported by a 'scientific approach', sometimes called a decision analysis. The analyst in charge of this preparation faces many diverse tasks: stakeholders identification, problem statement, elaboration of a list of possible actions, definition of one or several criteria for evaluating these actions, information gathering, sensitivity analysis, elaboration of a recommendation (for instance a ranking of the actions or a subset of 'good' actions), etc. The desire or necessity to take multiple conflicting viewpoints into account for evaluating the actions often makes this task even more difficult. In that case, we speak of multicriteria decision aiding [POM 93, ROY 85, VIN 89]. The expert must then try to synthesize the partial preferences (modeled by each criterion) into a global preference on which a recommendation can be based. This is called preference aggregation.
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Multicriteria decision aid methods are used to analyze decision problems including a series of alternative decisions evaluated on several criteria. They most often assume that perfect information is available with respect to the evaluation of the alternative decisions. However, in practice, imprecision, uncertainty or indetermination are often present at least for some criteria. This is a limit of most multicriteria methods. In particular the PROMETHEE methods do not allow directly for taking into account this kind of imperfection of information. We show how a general framework can be adapted to PROMETHEE and can be used in order to integrate different imperfect information models such as a.o. probabilities, fuzzy logic or possibility theory. An important characteristic of the proposed approach is that it makes it possible to use different models for different criteria in the same decision problem.
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European Journal of Operational Research, 2007
Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making in problems with inaccurate, uncertain, or missing information. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one, or that would give a certain rank for a specific alternative. The main results of the analysis are rank acceptability indices, central weight vectors and confidence factors for different alternatives. The rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative, the central weight vectors represent the typical preferences favouring each alternative, and the confidence factors measure whether the criteria measurements are sufficiently accurate for making an informed decision.