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.