A redundancy measure for efficient fuzzy rule-base reduction

Driven by the growing complexity of real-world systems, current trends in fuzzy system modeling employ ways to automatically learn the system rule-base from numerical data. While these approaches greatly improve model accuracy, the resulting rule-base is generally less interpretable than expert-driven rule-bases. We provide qualitative justification for this behavior and show that automatic rule-base generation leads to the occurrence of redundant rules, i.e. rules encoding approximately the same knowledge. In order to improve interpretability, redundant rules must be properly detected and removed. Therefore, this paper introduces a novel measure to estimate the redundancy of fuzzy rules based on the common influence exerted by a pair of rules over the data, and weighted by some distance measure between rules. The concept of common influence, defined therein, indicates how two rules are linked by the data distribution. Our approach is validated on some analytical function modeling task and then tested on a real-world problem dealing with vibrotactile stimuli characterization. Both experiments showed that removing the most redundant rules, according to the proposed redundancy measure, yields smaller rule-bases of up to 25%, with only negligible drops in accuracy.