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Interpretabilty is one of the desired characteristics in various classification task. Rule-based system and fuzzy logic can be used for interpretation in classification. The main drawback of rule-based system is that it may contain large complex rules for classification and sometimes it becomes very difficult in interpretation. Rule reduction is also difficult for various reasons. Removing important rules may effect in classification accuracy. This paper proposes a hybrid fuzzy-rough set approach named RS-HeRR for the generation of effective, interpretable and compact rule set. It combines a powerful rule generation and reduction fuzzy system, called Hebbian-based rule reduction algorithm (HeRR) and a novel rough-set-based attribute selection algorithm for rule reduction. The proposed hybridization leverages upon rule reduction through reduction in partial dependency as well as improvement in system performance to significantly reduce the problem of redundancy in HeRR, even while providing similar or better accuracy. RS-HeRR demonstrates these characteristics repeatedly over four diverse practical classification problems, such as diabetes identification, urban water treatment monitoring, sonar target classification, and detection of ovarian cancer. It also demonstrates excellent performance for highly biased datasets. In addition, it competes very well with established non-fuzzy classifiers and outperforms state-of-the-art methods that use rough sets for rule reduction in fuzzy systems.

RS-HeRR: a rough set-based Hebbian rule reduction neuro-fuzzy system