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Multi-criteria decision making (MCDM) deals with decisions involving the choice of the best alternative among several potential candidates in a decision. Every decision requires the balancing of multiple factors, the criteria, which is done sometimes explicitly, sometimes without conscious consideration. Decision might be a simple choice between two or more well-defined alternatives; however, often, decision problems are rather complex problems covering information of complex and conflicting nature reflecting differing perspectives. It is under these conditions that the tools and methods presented in this chapter come into play. We reviewed a number of methods that have been widely used to facilitate the structuring and understanding of the perceived decision problem. We started with the simplest approaches, such as the Pareto optimality and the simple additive ranking approach followed by the approaches belonging to the so-called multiattribute value theory, that is, utility, desirability, and dominance functions. In these models, numerical scores are constructed to represent the degree to which an alternative may be preferred to another. These scores are developed initially for each criterion and are aggregated into a higher level of preference models. The outranking model category, which includes PROMETHEE, ELECTRE, and ORESTE (Organisation, Rangement Et Synthèse de données relaTionElles) methods, is then presented. In these methods, alternatives are compared pairwise, initially in terms of each criterion and then the preference information is aggregated across all the criteria. These methods attempt to set up the strength of evidence in favor of one alternative over the others. A fairly detailed description of the methods ELECTRE I, II, and III is provided to illustrate its evolution from a simple method to a quite sophisticated method. The Hasse diagram technique is illustrated as an example of partial order ranking (POR) methods, which are vectorial approaches that recognize that different criteria are not always in agreement, but can be conflicting, which means that not all the alternatives can be directly compared with others. This approach not only ranks alternatives but also identifies contradictions in the criteria used for ranking, allowing the so-called incomparable condition where some residual order remains. The chapter also provides a short overview of the goal programming approach. The theoretical background of each of these models is presented together with the practical implementation of some of these methods provided as an illustrative example.

Pavan, M., & Todeschini, R. (2009). Multicriteria Decision Making Methods. In S.D. Brown, R. Tauler, & B. Walczak (a cura di), Comprehensive Chemometrics (pp. 591-629). Elsevier.

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