Abstract
This chapter deals with a crucial step in the decision aiding process: the aggregation of the alternatives’ performances on each criterion in order to faithfully model the overall preference of the decision maker. The approach we follow is that of conjoint measurement, which aims at determining under which conditions a preference can be represented in a particular aggregation model. This approach is first illustrated with the classical additive value function model. Then, we describe two broad families of preference models, which constitute a framework encompassing many aggregation models used in practice. The aggregation rules that fit with the second family of models rely on the aggregation of preference differences. Among this family we find, in particular, models for the outranking relations (concordance relations with vetoes) that are used in several case studies in this book.
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Notes
- 1.
This postulates the extension to all the Cartesian product X of the preference relation that is perceived on \(\overline{g}(A) = \left \{(g_{1}(a),\ldots,g_{n}(a)),\ a \in A\right \}\). In practice, such an extension could force the client to compare alternatives that appear artificial or unrealistic to him. Despite possible unwanted practical consequences and provided that the range X i is not unrealistic, we consider that the extension of \(\succapprox\) to X is not an outrageous assumption.
- 2.
In reality, these values have been determined by means of another elicitation method; details are provided in Bouyssou et al. (2000, ch. 6).
- 3.
- 4.
In case of a tie, i.e. whenever \((x_{i},y_{i})\sim _{i}^{{\ast}}(z_{i},w_{i})\), one has however to look explicitly at the relation between the reverse differences \((y_{i},x_{i})\) and \((w_{i},z_{i})\) since all cases (\(\succapprox _{i}^{{\ast}}\), \(\sim _{i}^{{\ast}}\) or \(\precapprox _{i}^{{\ast}}\)) can possibly show up.
- 5.
The lexicographic preference described in Sect. 3.4.5.4 enters into this framework but can be seen as a limit case.
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Bouyssou, D., Marchant, T., Pirlot, M., Tsoukiàs, A., Vincke, P. (2015). Modelling Preferences. In: Bisdorff, R., Dias, L., Meyer, P., Mousseau, V., Pirlot, M. (eds) Evaluation and Decision Models with Multiple Criteria. International Handbooks on Information Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46816-6_3
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