Abstract
A key problem in Multiple-Criteria Decision Making is how to measure the importance of the different criteria when just a partial preference relation among actions is given. In this note we address the problem of constructing a linear score function (and thus how to associate weights of importance to the criteria) when a binary relation comparing actions and partial information (relative importance) on the criteria are given. It is shown that these tasks can be done viaSupport Vector Machines, an increasingly popular Data Mining technique, which reduces the search of the weights to the resolution of (a series of) nonlinear convex optimization problems with linear constraints. An interactive method is then presented and illustrated by solving a multiple-objective 0–1 knapsack problem. Extensions to the case in which data are imprecise (given by intervals) or intransitivities in strict preferences exist are outlined.
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Partially supported by grants MTM2005-09362-103-01 of MEC, Spain, and FQM-329 of Junta de Andalucía, Spain. Part of this work has been written while the author visited the Department of Statistics and Decision Support Systems of the Universität Wien.
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Carrizosa, E. Deriving weights in multiple-criteria decision making with support vector machines. TOP 14, 399–424 (2006). https://doi.org/10.1007/BF02837570
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DOI: https://doi.org/10.1007/BF02837570
Key words
- Linear score functions
- support vector machines
- multiple-criteria decision making with partial information
- data mining