An integer programming approach for fuzzy rule-based classification systems

Fuzzy rule-based classification systems (FRBCSs) have been successfully employed as a data mining technique where the goal is to discover the hidden knowledge in a data set in the form of interpretable rules and develop an accurate classification model. In this paper, we propose an exact approach to learn fuzzy rules from a data set for a FRBCS. First, we propose a mixed integer programming model that extracts optimal fuzzy rules from a data set. The model's embedded feature selection allows absence of insignificant features in a fuzzy rule in order to enhance its accuracy and coverage. In order to build a comprehensive Rule Base (RB), we use this model in an iterative procedure that finds multiple rules by converting the obtained optimal solutions into a set of taboo constraints that prevents the model from re-finding the previously obtained rules. Furthermore, it changes the search direction by temporarily removing the correctly predicted patterns from the training set aiming to find the optimal rules that predict uncovered patterns in the training set. This procedure ensures that most of the patterns in the training set are covered by the RB. Next, another mixed integer programming model is developed to maximize predictive accuracy of the classifier by pruning the RB and removing redundant rules. The predictive accuracy of the proposed model is tested on the benchmark data sets and compared with the state-of-the-art algorithms from the literature by non-parametric statistical tests.