Noise reduction with inference based on fuzzy rule interpolation at an infinite number of activating points: A feasibility study

A method for noise reduction is proposed on the basis of a fuzzy-inference scheme for sparse rule bases called α-GEMINAS (a-level-set and generalizedmean-based inference with fuzzy rule interpolation at an infinite number of activating points). The noisereduction process in the proposed method is decisive and is expected to improve the robustness to noise in fuzzy-rule optimization, less relying on trial-anderror-based progress. The proposed method reduces noise in learning data by iteratively performing a-GEMINAS. Initial fuzzy rules for α-GEMINAS are determined by the learning data themselves and the input values of the learning data are given as facts for α-GEMINAS. Deduced consequences replace the consequent singletons in the fuzzy rules. This process is repeated and the noise is reduced along with the iterations. Simulation results indicate that noise is reduced by large amounts in the early iterations and the reduction rate is decelerated in the later iterations where the deviations in the learning data are suppressed to a great extent. These properties prove that the proposed method is feasible in practice.