A Novel Approach for Combining Fuzzy Rules Using Mean Operators for Effective Rule Reduction

This paper will present a novel method based on harmonic mean, geometric mean, arithmetic mean and root mean square to help reduce fuzzy rules. The objective of the new method proposed is to produce fuzzy models with both a small number of interpretable rules and sufficiently high precision. Comparisons will be made between systems utilizing reduced rules and original rules to verify efficacy of the new methods in terms of the defuzzified outputs. As a practical example of a nonlinear system, an inverted pendulum will be controlled by a minimal set of rules to illustrate the performance and applicability of the proposed method.