Tomada de decisão multicritério: lidando com interações entre critérios por meio da análise de variáveis latentes

Author(s)

Guilherme Dean Pelegrina

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Faculdade de Engenharia Elétrica e de Computação
• Defense date: 2020-11-27

Examining board members

João Marcos Travassos Romano; Denis Bouyssou; Michel Grabisch; Christian Jutten; Aline de Oliveira Neves Panazio

• Advisor: João Marcos Travassos Romano; Leonardo Tomazeli Duarte

Abstract

A typical problem in multicriteria decision making consists in ranking a set of alternatives according to their evaluations by a set of criteria. Aiming at dealing with this problem, several methods were developed in the literature. However, most of them were not conceived in order to consider structural information contained within the collected decision data. For instance, redundancies among criteria is frequently observed in practical situations, which may bias the achieved ranking. In this Ph.D. thesis, we propose novel methods that can be used to deal with redundant criteria. An interesting aspect is that the redundancy may be explained by latent factors that are associated with two or more criteria simultaneously. In other words, the collected evaluations consist in a mixture of latent data. Therefore, we may formulate the addressed problem as a blind source separation one and extract the relevant information used to recover these data. We use this information to improve existing methods in order to mitigate biased results and achieve a fairer ranking of alternatives. Moreover, we also use this information to adjust the weighted arithmetic mean parameters. Our experiments attest that the proposed approach penalizes redundant criteria by decreasing their associated weights. Therefore, the impact of such a redundancy in the obtained ranking is softened. We also revisit two aggregation functions that model intercriteria relations, the Choquet integral and the multilinear model. However, we could note that few works have been conducted in the context of the latter one. Therefore, in this study, we provide both theoretical results, by formulating the 2-additive multilinear model, and experimental results, by applying supervised and unsupervised approaches for capacity identification. In supervised approaches, we consider regularization terms in the optimization model, which may lead to a capacity close to the additive or 2-additive ones. With respect to the unsupervised approaches, we associate some parameters to similarity measures among criteria and to a measure of how a set of criteria impacts on the output function, called Sobol¿ index. The parameters obtained by our proposals led to unbiased overall evaluations. Other than the multicriteria problem, we also may be concerned with situations involving multiple decision makers. In this case, one may have interactions among criteria and among individuals. In this study, we investigate methods that are able to adjust the weights used in the weighted arithmetic mean in order to penalize both correlated criteria and ''correlated'' decision makers, i.e., individuals that may not be acting independently from the other ones. Another analysis that we conduct is the application of the Choquet integral to model interactions among criteria and among decision makers. In this case, we exploit an alternative representation for the multilevel Choquet integral and investigate if the 2-step aggregation procedure commutes. Based on our experiments and the interesting achieved results, we aim at contributing to the discussion on the use of latent variable analysis techniques in multicriteria decision making problems and motivating the development of future works on this subject (AU)

• FAPESP's process: 16/21571-4 - Multigroup and multiple criteria decision analysis methods: models based on information processing
• Grantee: Guilherme Dean Pelegrina
• Support Opportunities: Scholarships in Brazil - Doctorate