Autor: Jonata Cristian Wieczynski (Currículo Lattes)
Resumo
The discrete Choquet integral is an averaging aggregation function which is commonly used in a variety of applications. Recently, a series of generalizations of the Choquet integral have been introduced, like the CT-integrals, CC-integrals, CF-integrals and d-Choquet integral. They were applied in diverse problems and have shown good results, compared with the standard Choquet integral. Two of those applications are classification, by using Fuzzy Rule-Based Classification Systems (FRBCS), and decision making, with the Group Modular Choquet Random Technique for Order by Preference to Ideal Solution (GMC-RTOPSIS). The FRBCS have been an extensively application of the generalizations of the Choquet integral, as they are quite explainable and their results are good. On the other hand, the GMC-RTOPSIS is a multi-criteria decision making method, which is able to process multiple types of data as input, as well as dealing with interaction among the pre-established criteria via the standard Choquet integral. The first objective of this Master's thesis was to use the already developed theory of CT- and CC-integrals in decision making. We have applied them in the GMC-RTOPSIS in place of the standard Choquet integral. The second was to develop the concept of dCF-integral, a generalization of the Choquet integral based on functions F, from the CF-integral, and dissimilarity functions, from the d-Choquet integral. We also tested the applicability of the dCF-integral in classification and decision making problems. Lastly, the CT- and CC-integrals showed a better separation when using functions other than the product. In both of the methods the Lukasiewicz t-norm/copula performed better in distinguishing the top of the rank. When applying the dCF-integrals in classification problems, we obtained better results for some combinations of functions F and dissimilarities than using the CF-integrals. This is also seen in the decision making method GMC-RTOPSIS, which presented a higher separation of the alternatives when using the dCF-integrals in comparison to using CT-, CC- and the standard Choquet integral.