Abstract
We suppose that all we know about the preferences of an agent, is given by a (small) collection of relative preferences between choices represented by their evaluations on a set of criteria. Taking lesson from the success of the use of analogical proportions for predicting the class of a new item from a set of classified examples, we explore the possibility of using analogical proportions for completing a set of relative preferences. Such an approach is also motivated by a striking similarity between the formal structure of the axiomatic characterization of weighted averages and the logical definition of an analogical proportion. This paper discusses how to apply an analogical proportion-based approach to the learning of relative preferences, assuming that the preferences are representable by a weighted average, and how to validate experimental results. The approach is illustrated by examples.
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Notes
- 1.
Note that “preference difference” is not to be confused with “arithmetic difference”. For example, a person who wants to buy a car at a maximal price of 20 k€ will in general consider that an arithmetic difference of 1 k€ between 19 and 20 k€ is a worse preference difference than the same arithmetic difference between 14 and 15 k€.
- 2.
A and B suggest that the difference of preference (3, 1) on the third criterion (comfort) is “larger” (or more important) than the difference of preference (4, 3) on the same criterion. Given C, assuming that (2, 3, 3) is not preferred to (4, 1, 1) would reveal contradictory tradeoffs since it implies that, in this context, the difference of preference (4, 3) on the third criterion is larger than (3, 1).
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Pirlot, M., Prade, H., Richard, G. (2016). Completing Preferences by Means of Analogical Proportions. In: Torra, V., Narukawa, Y., Navarro-Arribas, G., Yañez, C. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2016. Lecture Notes in Computer Science(), vol 9880. Springer, Cham. https://doi.org/10.1007/978-3-319-45656-0_12
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