Noise reduction with fuzzy inference based on generalized mean and singleton input–output rules: A feasibility study

A method is proposed for reducing noise in learning data on the basis of fuzzy inference methods called α-GEMII (α-level-set and generalized-mean-based inference with the proof of two-sided symmetry of consequences) and α-GEMINAS (α-level-set and generalized-mean-based inference with fuzzy rule interpolation at an infinite number of activating points). It is especially effective to reduce noise in randomly-sampled data, given by singleton input–output pairs, for fuzzy rule optimization. In the proposed method, α-GEMII and α-GEMINAS are performed with singleton input–output rules and facts defined by fuzzy sets (non-singletons). The rules are initially determined by the input–output pairs of the learning data. They are arranged with consequences deduced by α-GEMII and α-GEMINAS. Then, they are updated with consequences obtained in iteratively performing α-GEMINAS. The noise reduction in each iteration is a decisive process and thus the proposed method is expected to improve the robustness to noise in fuzzy rule optimization, relying less on trial-and-error-based progress. Simulation results show that noise is properly reduced in each iteration and the deviation in the learning data is suppressed to a great extent.