Abstract
In many ranking problems, some particular aspects of the addressed situation should be taken into account in the aggregation process. An example is the presence of correlations between criteria, which may introduce bias in the derived ranking. In these cases, aggregation functions based on a capacity may be used to overcome this inconvenience, such as the Choquet integral or the multilinear model. The adoption of such strategies requires a stage to estimate the parameters of these aggregation operators. This task may be difficult in situations in which we do not have either further information about these parameters or preferences given by the decision maker. Therefore, the aim of this paper is to deal with such situations through an unsupervised approach for capacity identification based on the multilinear model. Our goal is to estimate a capacity that can mitigate the bias introduced by correlations in the decision data and, therefore, to provide a fairer result. The viability of our proposal is attested by numerical experiments with synthetic data.
This work was supported by the São Paulo Research Foundation (FAPESP, grant numbers 2016/21571-4 and 2017/23879-9) and the National Council for Scientific and Technological Development (CNPq, grant number 311357/2017-2).
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Notes
- 1.
It is worth mentioning that the multilinear model generalizes the WAM, i.e., if we consider an additive capacity, \(F_{ML}(\cdot )\) is equivalent to \(F_{WAM}(\cdot )\).
- 2.
It is worth mentioning that we must satisfy the axioms of a capacity.
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Pelegrina, G.D., Duarte, L.T., Grabisch, M., Romano, J.M.T. (2020). An Unsupervised Capacity Identification Approach Based on Sobol’ Indices. In: Torra, V., Narukawa, Y., Nin, J., Agell, N. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2020. Lecture Notes in Computer Science(), vol 12256. Springer, Cham. https://doi.org/10.1007/978-3-030-57524-3_6
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