  Interpretability has always been a major concern for fuzzy rule-based
classifiers. The usage of human-readable models allows them to explain the
reasoning behind their predictions and decisions. However, when it comes to Big
Data classification problems, fuzzy rule-based classifiers have not been able
to maintain the good trade-off between accuracy and interpretability that has
characterized these techniques in non-Big Data environments. The most accurate
methods build too complex models composed of a large number of rules and fuzzy
sets, while those approaches focusing on interpretability do not provide
state-of-the-art discrimination capabilities. In this paper, we propose a new
distributed learning algorithm named CFM-BD to construct accurate and compact
fuzzy rule-based classification systems for Big Data. This method has been
specifically designed from scratch for Big Data problems and does not adapt or
extend any existing algorithm. The proposed learning process consists of three
stages: 1) pre-processing based on the probability integral transform theorem;
2) rule induction inspired by CHI-BD and Apriori algorithms; 3) rule selection
by means of a global evolutionary optimization. We conducted a complete
empirical study to test the performance of our approach in terms of accuracy,
complexity, and runtime. The results obtained were compared and contrasted with
four state-of-the-art fuzzy classifiers for Big Data (FBDT, FMDT, Chi-Spark-RS,
and CHI-BD). According to this study, CFM-BD is able to provide competitive
discrimination capabilities using significantly simpler models composed of a
few rules of less than 3 antecedents, employing 5 linguistic labels for all
variables.
