Open Access
Applying d-XChoquet integrals in classification problems
(IEEE, 2022) Wieczynski, Jonata; Lucca, Giancarlo; Borges, Eduardo N.; Emmendorfer, Leonardo R.; Ferrero Jaurrieta, Mikel; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Several generalizations of the Choquet integral have been applied in the Fuzzy Reasoning Method (FRM) of Fuzzy Rule-Based Classification Systems (FRBCS's) to improve its performance. Additionally, to achieve that goal, researchers have searched for new ways to provide more flexibility to those generalizations, by restricting the requirements of the functions being used in their constructions and relaxing the monotonicity of the integral. This is the case of CT-integrals, CC-integrals, CF-integrals, CF1F2-integrals and dCF-integrals, which obtained good performance in classification algorithms, more specifically, in the fuzzy association rule-based classification method for high-dimensional problems (FARC-HD). Thereafter, with the introduction of Choquet integrals based on restricted dissimilarity functions (RDFs) in place of the standard difference, a new generalization was made possible: the d-XChoquet (d-XC) integrals, which are ordered directional increasing functions and, depending on the adopted RDF, may also be a pre-aggregation function. Those integrals were applied in multi-criteria decision making problems and also in a motor-imagery brain computer interface framework. In the present paper, we introduce a new FRM based on the d-XC integral family, analyzing its performance by applying it to 33 different datasets from the literature.
Open Access
Explainable classification methods for fish species detection using hydroacoustic data
(IEEE, 2021) Costa, Lucas Tubino Bonifacio; Lucca, Giancarlo; Pereira Dimuro, Graçaliz; Borges, Eduardo N.; Emmendorfer, Leonardo R.; Weigert, Stefan Cruz; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
This work aims to evaluate explainable classification methods for the detection of fish species from hydroacoustic data acquired by echo sounders at a region near the coastline of south and southeastern Brazil. Decision trees and fuzzy rule-based methods were adopted. The fitted models were evaluated by quality measures based on the performance of the classifiers and also by an expert which analyzed the usefulness of the rules on describing the schools. The models learned by the algorithms performed well for the available data and were able to represent the documented behavior of the species considered in the studied region, according to the literature.
Open Access
Additively generated (a,b)-implication functions*
(IEEE, 2023) Santos, Helida; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Paiva, Rui; Lucca, Giancarlo; Moura, Bruno; Cruz, Anderson; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Some problems involving classification through neural networks are known to use inputs out of the scope of the unit interval. Therefore, defining operations on arbitrary closed real intervals may be an interesting strategy to tackle this issue and enhance those application environments. In this paper we follow the ideas already discussed in the literature regarding (a,b)-fusion functions, and (a,b)-negations, to provide a new way to construct implication functions. The main idea is to construct an operator using additively generated functions that preserve the properties required by implication functions.
Open Access
Exploring the relationships between data complexity and classification diversity in ensembles
(SciTePress, 2021) Formentín Garcia, Nathan; Tiggeman, Frederico; Borges, Eduardo N.; Lucca, Giancarlo; Santos, Helida; Pereira Dimuro, Graçaliz; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Several classification techniques have been proposed in the last years. Each approach is best suited for a particular classification problem, i.e., a classification algorithm may not effectively or efficiently recognize some patterns in complex data. Selecting the best-tuned solution may be prohibitive. Methods for combining classifiers have also been proposed aiming at improving the generalization ability and classification results. In this paper, we analyze geometrical features of the data class distribution and the diversity of the base classifiers to understand better the performance of an ensemble approach based on stacking. The experimental evaluation was conducted using 32 real datasets, twelve data complexity measures, five diversity measures, and five heterogeneous classification algorithms. The results show that stacked generalization outperforms the best individual base classifier when there is a combination of complex and imbalanced data with diverse predictions among weak learners.
Open Access
On the generalizations of the Choquet integral for application in FRBCs
(Springer, 2021) Lucca, Giancarlo; Borges, Eduardo N.; Berri, Rafael A.; Emmendorfer, Leonardo R.; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
An effective way to cope with classification problems, among others, is by using Fuzzy Rule-Based Classification Systems (FRBCSs). These systems are composed by two main components, the Knowledge Base (KB) and the Fuzzy Reasoning Method (FRM). The FRM is responsible for performing the classification of new examples based on the information stored in the KB. A key point in the FRM is how the information given by the fired fuzzy rules is aggregated. Precisely, the aggregation function is the component that differs from the two most widely used FRMs in the specialized literature. In this paper we provide a revision of the literature discussing the generalizations of the Choquet integral that has been applied in the FRM of a FRBCS. To do so, we consider an analysis of different generalizations, by t-norms, copulas, and by F functions. Also, the main contributions of each generalization are discussed.
Open Access
Fuzzy integrals for edge detection
(Springer, 2023) Marco Detchart, Cedric; Lucca, Giancarlo; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; López Molina, Carlos; Borges, Eduardo N.; Rincón Arango, Jaime Andrés; Julian, Vicente; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this work, we compare different families of fuzzy integrals in the context of feature aggregation for edge detection. We analyze the behaviour of the Sugeno and Choquet integral and some of its generalizations. In addition, we study the influence of the fuzzy measure over the extracted image features. For testing purposes, we follow the Bezdek Breakdown Structure for edge detection and compare the different fuzzy integrals with some classical feature aggregation methods in the literature. The results of these experiments are analyzed and discussed in detail, providing insights into the strengths and weaknesses of each approach. The overall conclusion is that the configuration of the fuzzy measure does have a paramount effect on the results by the Sugeno integral, but also that satisfactory results can be obtained by sensibly tuning such parameter. The obtained results provide valuable guidance in choosing the appropriate family of fuzzy integrals and settings for specific applications. Overall, the proposed method shows promising results for edge detection and could be applied to other image-processing tasks.
Open Access
Application and comparison of CC-integrals in business group decision making
(Springer, 2022) Wieczynski, Jonata; Lucca, Giancarlo; Borges, Eduardo N.; Pereira Dimuro, Graçaliz; Lourenzutti, Rodolfo; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Optimized decisions is required by businesses (analysts) if they want to stay open. Even thought some of these are from the knowhow of the managers/executives, most of them can be described mathematically and solved (semi)-optimally by computers. The Group Modular Choquet Random Technique for Order of Preference by Similarity to Ideal Solution (GMC-RTOPSIS) is a Multi-Criteria Decision Making (MCDM) that was developed as a method to optimize the later types of problems, by being able to work with multiple heterogeneous data types and interaction among different criteria. On the other hand the Choquet integral is widely used in various fields, such as brain-computer interfaces and classification problems. With the introduction of the CC-integrals, this study presents the GMC-RTOPSIS method with CC-integrals. We applied 30 different CC-integrals in the method and analyzed its results using 3 different methods. We found that by modifying the decisionmaking method we allow for more flexibility and certainty in the choosing process.
Open Access
Application of the Sugeno integral in fuzzy rule-based classification
(Springer, 2022) Wieczynski, Jonata; Lucca, Giancarlo; Borges, Eduardo N.; Pereira Dimuro, Graçaliz; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Fuzzy Rule-Based Classification System (FRBCS) is a well known technique to deal with classification problems. Recent studies have considered the usage of the Choquet integral and its generalizations to enhance the quality of such systems. Precisely, it was applied to the Fuzzy Reasoning Method (FRM) to aggregate the fired fuzzy rules when classify new data. On the other side, the Sugeno integral, another well known aggregation operator, obtained good results when applied to brain-computer interfaces. Those facts led to the present study in which we consider the Sugeno integral in classification problems. That is, the Sugeno integral is applied in the FRM of a widely used FRBCS and its performance is analyzed over 33 different datasets from the literature. In order to show the efficiency of this new approach, the obtained results are also compared to past studies involving the application of different aggregation functions. Finally, we perform a statistical analysis of the application.
Open Access
General admissibly ordered interval-valued overlap functions
(CEUR Workshop Proceedings (CEUR-WS.org), 2021) Da Cruz Asmus, Tiago; Pereira Dimuro, Graçaliz; Sanz Delgado, José Antonio; Wieczynski, Jonata; Lucca, Giancarlo; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Overlap functions are a class of aggregation functions that measure the verlapping degree between two values. They have been successfully applied in several problems in which associativity is not required, such as classification and image processing. Some generalizations of overlap functions were proposed for them to be applied in problems with more than two classes, such as 𝑛- dimensional and general overlap functions. To measure the overlapping of interval data, interval-valued overlap functions were defined, and, later, they were also generalized in the form of 𝑛-dimensional and general interval-valued overlap functions. In order to apply some of those concepts in problems with interval data considering the use of admissible orders, which are total orders that refine the most used partial order for intervals, 𝑛-dimensional admissibly ordered interval-valued overlap functions were recently introduced, proving to be suitable to be applied in classification problems. However, the sole construction method presented for this kind of function do not allow the use of the well known lexicographical orders. So, in this work we combine previous developments to introduce general admissibly ordered interval-valued overlap functions, while also presenting different construction methods and the possibility to combine such methods, showcasing the flexibility and adaptability of this approach, while also being compatible with the lexicographical orders.
Unknown
CC-separation measure applied in business group decision making
(SciTePress, 2021) Wieczynski, Jonata; Lucca, Giancarlo; Borges, Eduardo N.; Pereira Dimuro, Graçaliz; Lourenzutti, Rodolfo; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In business, one of the most important management functions is decision making The Group Modular Choquet Random TOPSIS (GMC-RTOPSIS) is a Multi-Criteria Decision Making (MCDM) method that can work with multiple heterogeneous data types. This method uses the Choquet integral to deal with the interaction between different criteria. The Choquet integral has been generalized and applied in various fields of study, such as imaging processing, brain-computer interface, and classification problems. By generalizing the so-called extended Choquet integral by copulas, the concept of CC-integrals has been introduced, presenting satisfactory results when used to aggregate the information in Fuzzy Rule-Based Classification Systems. Taking this into consideration, in this paper. we applied 11 different CC-integrals in the GMC-RTOPSIS. The results demonstrated that this approach has the advantage of allowing more flexibility and certainty in the choosing process by giving a higher separation between the first and second-ranked alternatives.