Marcos Evandro Cintra

The use of fuzzy decision trees for coffee rust warning in Brazilian crops

This paper proposes the use of fuzzy decision trees for coffee rust warning, the most economically important coffee disease in the world. The models were induced using field data collected during 8 years. Using different subsets of attributes from the original data, three distinct datasets were constructed. The class attribute, representing the monthly infection rate, was used to construct six datasets according to two distinct infection rates. Induced models can be used to trigger alerts when estimated monthly disease infection rates reach one of the two thresholds. The first threshold allows applying preventive actions, whereas the second one requires a curative action. The fuzzy decision tree models were compared to the ones induced by a classic decision tree algorithm, taking into account the accuracy and the syntactic complexity of the models, as well as its quality according to an expert opinion. The fuzzy models showed better accuracy power and interpretability.

Fuzzy Rules Generation using Genetic Algorithms with Self-adaptive Selection

The definition of the Rule Base is one of the most important and difficult tasks when designing Fuzzy Systems. A method for the generation of fuzzy rule bases using genetic algorithm, including a phase of preselection of candidate rules, has been proposed by the authors. The selection of candidate rules uses criteria based on heuristics related to the degree of coverage of the rules. This paper proposes the use of a self-adaptive algorithm for the fitness calculation in the genetic algorithm, as an improvement of the referred method. The algorithm proposed emphasises the usefulness of compact rule bases as a means of transparency enhancement. Some experiment results are presented with a brief discussion of the advantages of the proposal.

Fuzzy Feature Subset Selection Using the Wang & Mendel Method

The dimension of a knowledge domain can impact the use of genetic algorithms to automatically design fuzzy rule bases, since the search space for the genetic algorithm increases exponentially with the number of features. Filters are a possible approach to reduce the number of features. However, the filter approach does not take into consideration the particular aspects of fuzzy logic when selecting or ranking features. This work presents a method for feature subset selection using the Wang & Mendel method as the base for a wrapper. Experimental results are presented and discussed.

Genetic generation of fuzzy systems with rule extraction using formal concept analysis

Fuzzy classification systems have been widely researched with many approaches proposed in the literature. Several methods are available for the automatic definition of fuzzy classification systems, which basically comprehend two tasks: i) the definition of the attributes in terms of fuzzy sets, and ii) the generation of a rule set containing the domain knowledge, named fuzzy rule base. Genetic Fuzzy Systems are used to learn or tune in fuzzy classification systems. Some genetic approaches for learning the fuzzy rule base require the previous extraction of a set of rules to be used as the genetic search space. In this paper, we present the FCA-Based method, a proposal for the automatic generation of fuzzy rule bases, which extracts a set of rules using the formal concept analysis theory directly from data. After extracting the rules forming the genetic search space, FCA-Based uses a genetic algorithm to select the final rule base. The last step of the FCA-Based method is a rule pruning step in order to improve the interpretability of the fuzzy rule bases. The extraction of rules proposed for the FCA-Based algorithm presents polynomial complexity and does not require the predefinition of the number of rules to be extracted. As it extracts rules directly from data, the proposed method avoids the random extraction of rules. It also presents the advantage of automatically extracting rules with variable number of conditions in their antecedents. A feature subset selection method, specifically designed for fuzzy classification systems, is integrated into the FCA-Based method in order to reduce the search space of solutions. The FCA-Based method is detailed and compared to eight different rule-based fuzzy systems. Experimental results using 27 benchmark datasets and a 10-fold cross-validation strategy show that FCA-Based presents higher accuracy and statistically significant difference with seven of the eight compared methods.

Using fuzzy formal concepts in the genetic generation of fuzzy systems

Fuzzy classification systems have been widely researched in the literature. Genetic fuzzy systems combine the power of the global search of genetic algorithms with fuzzy systems to provide accurate and interpretable rule-based systems. In this paper, we present a new approach for the genetic generation of fuzzy systems. The novelty of our proposal, named FCA-Based method, is a hybrid combination of fuzzy formal concepts to extract rules to form the search space of a genetic algorithm. FCA-Based extracts rules from existing data using the fuzzy formal concept analysis theory. FCA-Based uses the set of a priori extracted rules to form the final fuzzy rule bases by means of its genetic process. FCA-Based was tested using 10 datasets and a 10-fold cross-validation strategy using 4 different fuzzy data bases. The main comparisons included in this work are related to the number of extracted rules forming the genetic search spaces between FCA-BASED and DOC-BASED. Results are then analysed according to their accuracy and intepretability. The obtained results are adequate for the tested datasets.

Feature Subset Selection Using a Fuzzy Method

This paper presents further experiments for the FUZZY-WRAPPER, a feature subset selection method based on the Wang & Mendel method to generate fuzzy rule bases. This method aims at providing a means of selecting features taking into consideration aspects of fuzzy logic based representations, such as number, shape, and distribution of fuzzy sets, and reasoning method. The main idea is to consider different parameters from the general ones considered in the classic filter approaches, which are widely used for the task of feature subset selection. Experiments and results with 8 datasets, using a novel method to define the number of fuzzy sets for attributes, are presented and discussed.

On the estimation of the number of fuzzy sets for fuzzy rule-based classification systems

Defining the attributes in terms of fuzzy sets is an essential part in designing a fuzzy system. The main tasks involved in defining the fuzzy data base include deciding the type of fuzzy set (triangular, trapezoidal, etc), the number of fuzzy sets for each attribute, and their distribution in each attribute domain. In the absence of an expert, these definitions can be done empirically or by using automatic methods. In this paper, we present four different methods to estimate the number of fuzzy sets for a dataset. The first defines the same number of fuzzy sets for all attributes, while the other three flexibly estimate different numbers of fuzzy sets for each attribute of a given dataset. The aim of this paper is to provide fast and practicable methods to define fuzzy data bases, previously to the generation of the fuzzy rule base by more costly approaches, such as genetic fuzzy systems. These methods are evaluated using the FuzzyDT method, which generates a fuzzy decision tree based on the C4.5 classic method, on 11 datasets. The results are compared in terms of accuracy and number of generated rules. The results showed that the flexible estimation of the number of fuzzy sets obtained better error rates for the datasets used in the experiments.

Feature Subset Selection for Fuzzy Classification Methods

The automatic generation of fuzzy systems have been widely investigated with several proposed approaches in the literature. Since for most methods the generation process complexity increases exponentially with the number of features, a previous feature selection can highly improve the process. Filters, wrappers and embedded methods are used for feature selection. For fuzzy systems it would be desirable to take the fuzzy granulation of the features domains into account for the feature selection process. In this paper a fuzzy wrapper, previously proposed by the authors, and a fuzzy C4.5 decision tree are used to select features. They are compared with three classic filters and the features selected by the original C4.5 decision tree algorithm, as an embedded method. Results using 10 datasets indicate that the use of the fuzzy granulation of features domains is an advantage to select features for the purpose of inducing fuzzy rule bases.

An Evaluation of Rule-Based Classification Models Induced by a Fuzzy Method and Two Classic Learning Algorithms

Classification is a widely researched area in the machine learning and fuzzy communities with several approaches proposed by both communities. Some of the most relevant rule-based approaches from the machine learning community might include decision trees and rule inducers. The fuzzy community has also proposed many rule-based approaches, such as fuzzy decision trees and genetic fuzzy systems. This paper aims at comparing the models generated by rule-based methods for classification from both communities in terms of accuracy, and the induced rule set in terms of the syntactic complexity, taking into account the number of rules and average number of conjunctions in those rules. In general, models with lower syntactic complexity also show better interpretability, which is an important issue in knowledge acquisition. Results, using 10 datasets, a fuzzy C4.5 algorithm and two classic machine learning algorithms (C4.5 and PART), show that the fuzzy approach is able to produce lower error rates. Regarding the syntactic complexity of the models, PART produces in most cases the simplest models, although learning from different sets of features selected by filters. However, these simple models do not necessarily show a low error rate. Nevertheless, the induced fuzzy models inherit, from the fuzzy logic, the embedded ability of processing uncertainty and imprecision, avoiding the creation of rules using unnatural divisions of the attributes as the classic algorithms might do.

Fuzzy Rule Base Generation through Genetic Algorithms and Bayesian Classifiers A Comparative Approach

The definition of the fuzzy rule base is one of the most important and difficult tasks when designing fuzzy systems. This paper discusses the results of two different hybrid methods investigated earlier, for the automatic generation of fuzzy rules from numerical data. One of the methods proposes the creation of fuzzy rule bases using genetic algorithms in association with a heuristic for preselecting candidate rules. The other, named Bayes fuzzy, induces a Bayes classifier using a dataset previously granulated by fuzzy partitions and then translates this classifier into a fuzzy rule base. A comparative analysis between both approaches focusing on their main characteristics, strengths/weaknesses and easiness of use is carried out. The reliability of both methods is also compared by analyzing their results in a few knowledge domains.