Abstract
This chapter briefly presents a number of techniques that can be used to build recommendations in each of three classical problem statements (choosing, ranking, and sorting) on the basis of a preference model. We start with the simple case of a preference model based on a value function. We then turn to more complex cases.
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Notes
- 1.
This is true when A is finite. The general case may be more tricky: while the relation ≥ on \(\mathbb{R}\) is complete and transitive, \(G(\geq, \mathbb{R})\) is clearly empty. The same is true with ≥ on the open \(\left ]0, 1\right [\) interval.
- 2.
That is, π k+1 is at least as good as π k on all criteria and strictly better on some criterion.
- 3.
That is, it is strictly better on all criteria.
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Bouyssou, D., Marchant, T., Pirlot, M., Tsoukiàs, A., Vincke, P. (2015). Building Recommendations. 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_4
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