The multilinear model in multicriteria decision making: The case of 2-additive capacities and contributions to parameter identification

Guilherme Dean Pelegrina (1, 2, 3) , Leonardo Tomazeli Duarte (2) , Michel Grabisch (3, 4) , João Marcos Travassos Romano (5)

1 DSPCom - Laboratory of Signal Processing for Communications
2 UNICAMP - Universidade Estadual de Campinas = University of Campinas
3 CES - Centre d'économie de la Sorbonne
4 PSE - Paris School of Economics
5 UnB - University of Brasilia [Brazil]

In several multicriteria decision making problems, it is important to consider interactions among criteria in order to satisfy the preference relations provided by the decision maker. This can be achieved by using aggregation functions based on fuzzy measures, such as the Choquet integral and the multilinear model. Although the Choquet integral has been studied in a large number of works, one does not find the same literature with respect to the multilinear model. In this context, the contribution of this work is twofold. We first provide a formulation of the multilinear model by means of a 2-additive capacity. A second contribution lies in the problem of capacity identification. We consider a supervised approach and apply optimization models with and without regularization terms. Results obtained in numerical experiments with both synthetic and real data attest the performance of the considered approaches.

Mots clés: 2-additive capacity; capacity identification; multilinear model; multi-attribute utility theory; multiple criteria analysis

Domaines: Economies et finances; Mathématique discrète [cs.DM]

Guilherme Dean Pelegrina, Leonardo Tomazeli Duarte, Michel Grabisch, João Marcos Travassos Romano. The multilinear model in multicriteria decision making: The case of 2-additive capacities and contributions to parameter identification. European Journal of Operational Research, 2020, 282, pp.945-956. ⟨10.1016/j.ejor.2019.10.005⟩. ⟨halshs-02379646⟩