Noise reduction with fuzzy inference based on generalized mean and singleton input-output rules: Toward fuzzy rule learning in a unified inference platform

A method is proposed for reducing noise in learning data based on 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 particularly effective for reducing 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 set by directly using the input-output pairs of the learning data. They are arranged with the facts and consequences deduced by α-GEMII and α-GEMINAS. This process reduces noise to some extent and transforms the randomly sampled data into regularly sampled data for iteratively reducing noise at a later stage. The width of the regular sampling interval can be determined with tolerance so as to satisfy application-specific requirements. Then, the singleton input-output rules are updated with consequences obtained in iteratively performing α-GEMINAS for noise reduction. The noise reduction in each iteration is a deterministic process, and thus the proposed method is expected to improve the noise robustness in fuzzy rule optimization, relying less on trial-anderror-based progress. Simulation results demonstrate that noise is properly reduced in each iteration and the deviation in the learning data is suppressed considerably.