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

• DOI: 10.1016/j.ejor.2019.10.005
• Publication Date: 2019-10-07T14:28:45Z
• Authors: Guilherme Dean Pe...; Leonardo Tomazeli...; Michel Grabisch; João Marcos Trava...
• Keywords: capacity identification; 330; multiple criteria analysis; multi-attribute utility theory; 0211 other engineering and technologies; 02 engineering and technology; [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]; [SHS.ECO]Humanities and Social Sciences/Economics and Finance; multilinear model; 004; [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]; 2-additive capacity; [SHS.ECO] Humanities and Social Sciences/Economics and Finance

Abstract 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.