To address learning problems in which many examples and variables are involved, the use of algorithms that are capable of processing the data using simple and efficient techniques is required. The Wang and Mendel algorithm applied to classification (also known as the Chi algorithm) satisfies these properties in many cases. However, in particularly complex problems, such as those provided by big data, it has become necessary to use architectures for parallel processing, such as MapReduce, whose base algorithm is just this algorithm. The use of these architectures is necessary because the bottleneck of the algorithm is the calculation of the weight of the rules. This calculation requires, for each selected rule, to consider the adaptation of all the examples with this rule. Although this calculation is polynomial-order, in problems with many examples and where many rules are generated, it is very time consuming. In this article, we propose Quick Chi (QChi), a new algorithm based on the Wang–Mendel algorithm that uses, among other changes to make it efficient, a new way of calculating the weights of the rules that is much less computationally expensive. The reduction in learning time is so significant that it allows the algorithm to tackle big data problems without parallel processing structures. In addition to the description of the algorithm, this article checks experimentally on a wide variety of problems, including those that other authors have used as big data problems that this algorithm drastically reduces the learning time while maintaining the classification performance.

The Chi algorithm has been used in many applications to obtain a set of fuzzy rules from the data. Its main advantage is that it requires low learning time in relation to others learning algorithms and that makes it a good candidate for tackling Big Data problems. However, this algorithm has some shortcomings, among them, its limited generalization capability, which leads to obtaining a high number of uncovered examples over new unseen examples. An improved version of this algorithm is presented in this paper. The main difference lies in the process of assigning a candidate rule to each example, the original algorithm assigns only one, and in the new proposal, several rules are assigned. The inclusion of more rules improves the generalization capacity of the acquired knowledge, which in turn leads to an improvement in accuracy. The paper includes an extensive experimental study to show the performance of the proposal.

Age estimation is a fundamental task in forensic anthropology for both the living and the dead. The procedure consists of analyzing properties such as appearance, ossification patterns, and morphology in different skeletonized remains. The pubic symphysis is extensively used to assess adults’ age-at-death due to its reliability. Nevertheless, most methods currently used for skeleton-based age estimation are carried out manually, even though their automation has the potential to lead to a considerable improvement in terms of economic resources, effectiveness, and execution time. In particular, explainable machine learning emerges as a promising means of addressing this challenge by engaging forensic experts to refine and audit the extracted knowledge and discover unknown patterns hidden in the complex and uncertain available data. In this contribution we address the automation of the decision making process of Todd’s pioneering age assessment method to assist the forensic practitioner in its application. To do so, we make use of the pubic bone data base available at the Physical Anthropology lab of the University of Granada. The machine learning task is significantly complex as it becomes an imbalanced ordinal classification problem with a small sample size and a high dimension. We tackle it with the combination of an ordinal classification method and oversampling techniques through an extensive experimental setup. Two forensic anthropologists refine and validate the derived rule base according to their own expertise and the knowledge available in the area. The resulting automatic system, finally composed of 34 interpretable rules, outperforms the state-of-the-art accuracy. In addition, and more importantly, it allows the forensic experts to uncover novel and interesting insights about how Todd’s method works, in particular, and the guidelines to estimate age-at-death from pubic symphysis characteristics, generally.

The Fuzzy Rule-Based Classification Systems (FR-BCS) are classification models that use fuzzy rules to represent knowledge. FBRCS are popular today, with numerous applications and studies of their behavior and efficiency. This work is dedicated to studying a method that allows the minimization of FBRCS generated by the Chi Algorithm, using the Quine-McCluskey method so that the number of generated rules can be reduced, without greatly altering the accuracy, thus improving the simplicity of the model.

Ordinal classification can be used for predicting an ordinal variable, i.e. a variable whose value exists on an arbitrary scale where the relative ordering between different values is significant. Ordinal classification problems are getting an important position in learning problems with examples such as studies on food quality or credit risks related to the financial obligations of a company. KEEL (Knowledge Extraction based on Evolutionary Learning) is an open source (GPLv3) Java software tool that can be used for a large number of different knowledge data discovery tasks. It contains a wide variety of computational intelligence algorithm implementations providing a good tool and scenario to assess and develop computational problems. Focusing on problems of nominal classification or regression, there is not a wide variety of software that addresses this type of problems. This work aims to facilitate the use of the fuzzy rule learning algorithm for ordinal classification (NSLVOrd) enabling its integration into the well-known software tool KEEL. The implementation and some instructions to execute NSLVOrd in KEEL are also detailed showing the ease of use for any KEEL user.

The analysis with a very high number of examples is a subject of growing interest that needs new algorithms \nand procedures. In this case, we study how the massive use of data affects the reasoning processes for classification \nproblems that make use of fuzzy rule-based systems. First, we describe the standard reasoning model \nand the operations associated with its use, and once it is verified that these calculations may be inefficient in \nsome cases we propose a new model to perform such calculations. Basically, the proposal eliminates the need \nto review all the rules in every inference process, generating the rule that best adapts to the particular example, \nwhich does not have to be part of the set of rules, and from it explore only the rules that have some effect on \nthe example. We make an experimental study that shows the interest of the proposal presented.

Incremental approaches may be used to speed up the learning process when a classification algorithm is dealing with Big Data bases. In this work we present a study on how the size and composition of the set of learning examples that are given to an incremental algorithm affect its behaviour.

The MapReduce paradigm is a programming model mainly thought to process big data sets. This model has recently been used in a new proposal of a linguistic fuzzy rule-based learning algorithm. One of the most important aspects of this proposal is the use of a parallel and distributed algorithm. An alternative to this parallel and distributed organization is the use of an incremental learning algorithm in a sequential schema. We propose an incremental algorithm to learn fuzzy classification rules based on this idea and we also demonstrate through the experimental study that the proposal is very competitive when it is applied to big data problems.

In this paper we propose two extensions of our previously introduced method DECO3R, a Fuzzy Rule-based Classification System (FRBCS). DECO3R stands for Differential Evolution based Cooperative and Competing learning of Compact FRBCS. It follows the Genetic Cooperative - Competitive Learning (GCCL) approach, and utilizes the Differential Evolution (DE) as its learning algorithm. Two novel schemes will be introduced, one which creates a number of parallel populations employing different DE strategies, and one inserting newly constructed features (relations and functions) in the antecedent part of the rules. These two new schemes, as well as the combination thereof, boost the performance of DECO3R, as evidenced by the results obtained, which were validated using non-parametric statistical tests.

The sequential covering strategy has been and still is a very common way to develop rule learning algorithms. This strategy follows a greedy procedure to learn rules, where, after each step one rule is obtained. Recently, we proposed a new sequential covering strategy that allowed the review of previously learned knowledge during the learning process itself. This review of knowledge allowed the algorithm to adapt to changes that may occur in the context of learning. Specifically, in this paper we consider the changes produced by the addition of new training examples, and therefore we make a proposal of incremental learning of fuzzy rules. We have performed several experiments to test the behavior of the proposal and the results have been very promising.

In recent years, some authors have approached the instance selection problem from a meta-learning perspective. In their work, they try to find relationships between the performance of some methods from this field and the values of some data-complexity measures, with the aim of determining the best performing method given a data set, using only the values of the measures computed on this data. Nevertheless, most of the data-complexity measures existing in the literature were not conceived for this purpose and the feasibility of their use in this field is yet to be determined. In this paper, we revise the definition of some measures that we presented in a previous work, that were designed for meta-learning based instance selection. Also, we assess them in an experimental study involving three sets of measures, 59 databases, 16 instance selection methods, two classifiers, and eight regression learners used as meta-learners. The results suggest that our measures are more efficient and effective than those traditionally used by researchers that have addressed the instance selection from a perspective based on meta-learning.

Different fuzzy rule-based learning algorithms use the sequential covering strategy. This model applies a problem decomposition strategy, in which the task of finding a complete rule base is reduced to a sequence of subproblems in each of which the solution is to add a single rule. Now, we are interested in introducing additional capabilities in this strategy in order to review the knowledge previously extracted. Thus, our main objective is that in each iteration instead of only being able to add rules, we can propose three different options: to add the best rule that increases the prediction capability of the rule base, to add the best rule that replaces one or more rules previously learned without loosing accuracy or do not add any rule, if the rule base can not be improved. The experimental results show that this proposal maintains the accuracy of the model as well as the average number of rules but significantly reducing the number of conditions per database, which means that rules are more general. Therefore, this new iterative scheme improves the interpretability of the model obtained.

Traditionally, fuzzy rule based models work with a fixed set of features to describe a particular problem. Our proposal is to use feature construction by means of functions in order to obtain new variables that allow us to get more information about the problem. In particular, we propose the use of previously defined functions over the input variables in the antecedent of the rules. This let us to know if a combination of variables is able to provide us with more information than each one of them separately. In addition, we use a structure that helps us to manage and also restrict the number of functions under consideration by the learning algorithm. We also present a new model of rule in order to represent this kind of knowledge by extending a basic learning fuzzy rule-based model. Finally, we show the experimental study associated with this work.

This paper presents a proposal for using feature construction in a fuzzy rule-based learning algorithm as a method to avoid working with a fixed set of features to describe a particular problem. The main purpose is to increase the amount of information extracted from initial variables to construct a model that has better prediction capability. This approach iteratively looks for the function that obtains the best adaptation level to the examples covered by a rule. If exists, this function is added both to the antecedent of the rule and to a specific structure called catalog of functions in order to be considered by the learning algorithm. For that, a model of rule is used in order to represent this kind of knowledge in combination with the catalog, which helps us to manage the functions that have ever been considered during the learning process. Finally, a comparative study of the results obtained with this approach is presented.

Two basic requirements of fuzzy modeling are the accuracy and simplicity of the knowledge obtained. In this study, we propose a genetic learning algorithm of fuzzy relational rules, that is, fuzzy rules that include fuzzy relations. Fuzzy relational rules allow us to obtain fuzzy models with a good interpretability-accuracy trade-off. Since, the inclusion of relations increases the accuracy keeping the interpretability but increasing the number of features to be considered in the learning process. We also present a model to reduce the additional complexity that occurs when using this new type of rules. Finally, we also present an experimental study that demonstrated the advantage of the use of relational fuzzy rules.

Genetic algorithms offer a powerful search method for a variety of learning tasks, and there are different approaches in which they have been applied to learning processes. Structural learning algorithm on vague environment (SLAVE) is a genetic learning algorithm that uses the iterative approach to learn fuzzy rules. SLAVE can select the relevant features of the domain, but when working with large databases the search space is too large and the running time can sometimes be excessive. We propose to improve SLAVE by including a feature selection model in which the genetic algorithm works with individuals (representing individual rules) composed of two structures: one structure representing the relevance status of the involved variables in the rule, the other one representing the assignments variable/value. For this general representation, we study two alternatives depending on the information coded in the first structure. When compared with the initial algorithm, this new approach of SLAVE reduces the number of rules, simplifies the structure of the rules and improves the total accuracy.

A very important problem associated with the use of learning algorithms consists of fixing the correct assignment of the initial domains for the predictive variables. In the fuzzy case, this problem is equivalent of define the fuzzy labels for each variable. In this work, we propose the inclusion in a learning algorithm, called SLAVE, of a particular kind of linguistic hedges as a way to modify the intial semantic of the labels. These linguistic hedges allow us both to learn and to tune fuzzy rules.

SLAVE is an inductive learning algorithm that uses concepts based on fuzzy logic theory. This theory has been shown to be a useful representational tool for improving the understanding of the knowledge obtained from a human point of view. Furthermore, SLAVE uses an iterative approach for learning based on the use of a genetic algorithm (GA) as a search algorithm. We propose a modification of the initial iterative approach used in SLAVE. The main idea is to include more information in the process of learning one individual rule. This information is included in the iterative approach through a different proposal of calculus of the positive and negative example to a rule. Furthermore, we propose the use of a new fitness function and additional genetic operators that reduce the time needed for learning and improve the understanding of the rules obtained.