Using fuzzy formal concepts in the genetic generation of fuzzy systems

Abstract

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.

Genetic generation of fuzzy knowledge bases: new perspectives

“…The FCA-BASED method was tested using 10 datasets from UCI -Machine Learning Repository (Frank and Asuncion, 2010) with a 10-fold crossvalidation strategy (Cintra et al, 2012c). Table 6.11 summarizes the dataset characteristics, presenting the total number of examples, total number of features, including the number of continuous and discrete features (in brackets), the number of classes, and the majority error (ME).…”

“…With the proposal of the FCA-BASED method in (Cintra et al, 2012c), we included it in our comparisons between fuzzy and classic methods. Our experiments evaluated two groups of rule learning methods for classification:…”

“…One of the main contribution of this work is the proposal of the FCA-BASED method for the genetic generation of fuzzy systems, which generates the genetic search space using the formal concept analysis theory to extract rules from data (Cintra et al, 2012c). The task of generating the genetic search space is investigated and published in (Majidian et al, 2011;Cintra et al, 2011d).…”

“…The Genetic Generation of Fuzzy Systems -Our main contribution to this area, which is also the main contribution of this work, is the proposal of the FCA-BASED method in (Cintra et al, 2012c). The FCA-BASED method extracts the rules forming the genetic search space from data, based on the theory of formal concept analysis, which was investigated and proposed in (Majidian et al, 2011;Cintra et al, 2011d,a).…”

“…A similar approach, named DOC-BASED, was proposed in (Cintra and Camargo, 2007a), where the pre-selection of candidate rules is based on the degree of coverage of the rules. Furthermore, in order to reduce the computational cost of the extraction process of the candidate rules, as well as for scalability sake, a method that extracts the candidate rules from data, using the formal concept analysis theory, the FCA-BASED method (Cintra et al, 2012c) was proposed. Both the DOC-BASED and the FCA-BASED methods are described in this chapter.…”