Open Access
Pre-aggregation functions: construction and an application
(IEEE, 2015) Lucca, Giancarlo; Sanz Delgado, José Antonio; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Mesiar, Radko; Kolesárová, Anna; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
In this work we introduce the notion of preaggregation function. Such a function satisfies the same boundary conditions as an aggregation function, but, instead of requiring monotonicity, only monotonicity along some fixed direction (directional monotonicity) is required. We present some examples of such functions. We propose three different methods to build pre-aggregation functions. We experimentally show that in fuzzy rule-based classification systems, when we use one of these methods, namely, the one based on the use of the Choquet integral replacing the product by other aggregation functions, if we consider the minimum or the Hamacher product t-norms for such construction, we improve the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators like the maximum and the Choquet integral.
Open Access
A first study on the use of interval-valued fuzzy sets with genetic tuning for classification with imbalanced data sets
(Springer, 2009) Sanz Delgado, José Antonio; Fernández, Alberto; Bustince Sola, Humberto; Herrera, Francisco; Automática y Computación; Automatika eta Konputazioa
Classification with imbalanced data-sets is one of the recent challenging problems in Data Mining. In this framework, the class dis- tribution is not uniform and the separability between the classes is often difficult. From the available techniques in the Machine Learning field, we focus on the use of Fuzzy Rule Based Classification Systems, as they provide an interpretable model for the end user by means of linguistic variables. The aim of this work is to increase the performance of fuzzy modeling by adding a higher degree of knowledge by means of the use of Interval- valued Fuzzy Sets. Furthermore, we will contextualize the Interval-valued Fuzzy Sets with a post-processing genetic tuning of the amplitude of their upper bounds in order to enhance the global behaviour of this methodology.
Open Access
Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning
(Elsevier, 2010) Sanz Delgado, José Antonio; Fernández, Alberto; Bustince Sola, Humberto; Herrera, Francisco; Automática y Computación; Automatika eta Konputazioa
Among the computational intelligence techniques employed to solve classification problems, Fuzzy Rule-Based Classification Systems (FRBCSs) are a popular tool because of their interpretable models based on linguistic variables, which are easier to understand for the experts or end-users. The aim of this paper is to enhance the performance of FRBCSs by extending the Knowledge Base with the application of the concept of Interval-Valued Fuzzy Sets (IVFSs). We consider a post-processing genetic tuning step that adjusts the amplitude of the upper bound of the IVFS to contextualize the fuzzy partitions and to obtain a most accurate solution to the problem. We analyze the goodness of this approach using two basic and well-known fuzzy rule learning algorithms, the Chi et al.’s method and the fuzzy hybrid genetics-based machine learning algorithm. We show the improvement achieved by this model through an extensive empirical study with a large collection of data-sets.
Open Access
Using the Choquet integral in the fuzzy reasoning method of fuzzy rule-based classification systems
(MDPI, 2013) Barrenechea Tartas, Edurne; Bustince Sola, Humberto; Fernández Fernández, Francisco Javier; Paternain Dallo, Daniel; Sanz Delgado, José Antonio; Automática y Computación; Automatika eta Konputazioa
In this paper we present a new fuzzy reasoning method in which the Choquet integral is used as aggregation function. In this manner, we can take into account the interaction among the rules of the system. For this reason, we consider several fuzzy measures, since it is a key point on the subsequent success of the Choquet integral, and we apply the new method with the same fuzzy measure for all the classes. However, the relationship among the set of rules of each class can be different and therefore the best fuzzy measure can change depending on the class. Consequently, we propose a learning method by means of a genetic algorithm in which the most suitable fuzzy measure for each class is computed. From the obtained results it is shown that our new proposal allows the performance of the classical fuzzy reasoning methods of the winning rule and additive combination to be enhanced whenever the fuzzy measure is appropriate for the tackled problem.
Open Access
Improving Michigan-style fuzzy-rule base classification generation using a Choquet-like Copula-based aggregation function
(CEUR Workshop Proceedings (CEUR-WS.org), 2021) Hinojosa-Cardenas, Edward; Sarmiento-Calisaya, Edgar; Camargo, Heloisa A.; Sanz Delgado, José Antonio; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA1926
This paper presents a modification of a Michigan-style fuzzy rule based classifier by applying the Choquet-like Copula-based aggregation function, which is based on the minimum t-norm and satisfies all the conditions required for an aggregation function. The proposed new version of the algorithm aims at improving the accuracy in comparison to the original algorithm and involves two main modifications: replacing the fuzzy reasoning method of the winning rule by the one based on Choquet-like Copula-based aggregation function and changing the calculus of the fitness of each fuzzy rule. The modification proposed, as well as the original algorithm, uses a (1+1) evolutionary strategy for learning the fuzzy rulebase and it shows promising results in terms of accuracy, compared to the original algorithm, over ten classification datasets with different sizes and different numbers of variables and clases.
Open Access
A genetic tuning to improve the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets: degree of ignorance and lateral position
(Elsevier, 2011) Sanz Delgado, José Antonio; Fernández, Alberto; Bustince Sola, Humberto; Herrera, Francisco; Automática y Computación; Automatika eta Konputazioa
Fuzzy Rule-Based Systems are appropriate tools to deal with classification problems due to their good properties. However, they can suffer a lack of system accuracy as a result of the uncertainty inherent in the definition of the membership functions and the limitation of the homogeneous distribution of the linguistic labels. The aim of the paper is to improve the performance of Fuzzy Rule-Based Classification Systems by means of the Theory of Interval-Valued Fuzzy Sets and a post-processing genetic tuning step. In order to build the Interval-Valued Fuzzy Sets we define a new function called weak ignorance for modeling the uncertainty associated with the definition of the membership functions. Next, we adapt the fuzzy partitions to the problem in an optimal way through a cooperative evolutionary tuning in which we handle both the degree of ignorance and the lateral position (based on the 2-tuples fuzzy linguistic representation) of the linguistic labels. The experimental study is carried out over a large collection of data-sets and it is supported by a statistical analysis. Our results show empirically that the use of our methodology outperforms the initial Fuzzy-Rule Based Classification System. The application of our cooperative tuning enhances the results provided by the use of the isolated tuning approaches and also improves the behavior of the genetic tuning based on the 3-tuples fuzzy linguistic representation.
Open Access
A proposal for tuning the α parameter in CαC-integrals for application in fuzzy rule-based classification systems
(Springer, 2020) Lucca, Giancarlo; Sanz Delgado, José Antonio; Pereira Dimuro, Graçaliz; Bedregal, Benjamin; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Estadística, Informática y Matemáticas
In this paper, we consider the concept of extended Choquet integral generalized by a copula, called CC-integral. In particular, we adopt a CC-integral that uses a copula defined by a parameter α, which behavior was tested in a previous work using different fixed values. In this contribution, we propose an extension of this method by learning the best value for the parameter α using a genetic algorithm. This new proposal is applied in the fuzzy reasoning method of fuzzy rule-based classification systems in such a way that, for each class, the most suitable value of the parameter α is obtained, which can lead to an improvement on the system's performance. In the experimental study, we test the performance of 4 different so called CαC-integrals, comparing the results obtained when using fixed values for the parameter α against the results provided by our new evolutionary approach. From the obtained results, it is possible to conclude that the genetic learning of the parameter α is statistically superior than the fixed one for two copulas. Moreover, in general, the accuracy achieved in test is superior than that of the fixed approach in all functions. We also compare the quality of this approach with related approaches, showing that the methodology proposed in this work provides competitive results. Therefore, we demonstrate that CαC-integrals with α learned genetically can be considered as a good alternative to be used in fuzzy rule-based classification systems.
Open Access
Fuzzy rule-based classification systems for multi-class problems using binary decomposition strategies: on the influence of n-dimensional overlap functions in the fuzzy reasoning method
(Elsevier, 2016) Elkano Ilintxeta, Mikel; Galar Idoate, Mikel; Sanz Delgado, José Antonio; Bustince Sola, Humberto; Automatika eta Konputazioa; Institute of Smart Cities - ISC; Automática y Computación
Multi-class classification problems appear in a broad variety of real-world problems, e.g., medicine, genomics, bioinformatics, or computer vision. In this context, decomposition strategies are useful to increase the classification performance of classifiers. For this reason, in a previous work we proposed to improve the performance of FARC-HD (Fuzzy Association Rule-based Classification model for High-Dimensional problems) fuzzy classifier using One-vs-One (OVO) and One-vs-All (OVA) decomposition strategies. As a result of an exhaustive experimental analysis, we concluded that even though the usage of decomposition strategies was worth to be considered, further improvements could be achieved by introducing n-dimensional overlap functions instead of the product t-norm in the Fuzzy Reasoning Method (FRM). In this way, we can improve confidences for the subsequent processing performed in both OVO and OVA. In this paper, we want to conduct a broader study of the influence of the usage of n-dimensional overlap functions to model the conjunction in several Fuzzy Rule-Based Classification Systems (FRBCSs) in order to enhance their performance in multi-class classification problems applying decomposition techniques. To do so, we adapt the FRM of four well-known FRBCSs (CHI, SLAVE, FURIA, and FARC-HD itself). We will show that the benefits of the usage of n-dimensional overlap functions strongly depend on both the learning algorithm and the rule structure of each classifier, which explains why FARC-HD is the most suitable one for the usage of these functions.
Open Access
Enhancing multi-class classification in FARC-HD fuzzy classifier: on the synergy between n-dimensional overlap functions and decomposition strategies
(IEEE, 2014) Elkano Ilintxeta, Mikel; Galar Idoate, Mikel; Sanz Delgado, José Antonio; Fernández, Alberto; Barrenechea Tartas, Edurne; Herrera, Francisco; Bustince Sola, Humberto; Automática y Computación; Automatika eta Konputazioa
There are many real-world classification problems involving multiple classes, e.g., in bioinformatics, computer vision or medicine. These problems are generally more difficult than their binary counterparts. In this scenario, decomposition strategies usually improve the performance of classifiers. Hence, in this paper we aim to improve the behaviour of FARC-HD fuzzy classifier in multi-class classification problems using decomposition strategies, and more specifically One-vs-One (OVO) and One-vs-All (OVA) strategies. However, when these strategies are applied on FARC-HD a problem emerges due to the low confidence values provided by the fuzzy reasoning method. This undesirable condition comes from the application of the product t-norm when computing the matching and association degrees, obtaining low values, which are also dependent on the number of antecedents of the fuzzy rules. As a result, robust aggregation strategies in OVO such as the weighted voting obtain poor results with this fuzzy classifier. In order to solve these problems, we propose to adapt the inference system of FARC-HD replacing the product t-norm with overlap functions. To do so, we define n-dimensional overlap functions. The usage of these new functions allows one to obtain more adequate outputs from the base classifiers for the subsequent aggregation in OVO and OVA schemes. Furthermore, we propose a new aggregation strategy for OVO to deal with the problem of the weighted voting derived from the inappropriate confidences provided by FARC-HD for this aggregation method. The quality of our new approach is analyzed using twenty datasets and the conclusions are supported by a proper statistical analysis. In order to check the usefulness of our proposal, we carry out a comparison against some of the state-of-the-art fuzzy classifiers. Experimental results show the competitiveness of our method.