Multi-Level Control of Fuzzy-Constraint Propagation in Inference with Fuzzy Rule Interpolation at an Infinite Number of Activating Points

This paper clarifies the relations in properties and structures between fuzzy inference methods based on α-cuts and the generalized mean. The group of the inference methods is named the α-GEM (α-cut and generalized-mean-based inference) family. A unified platform is proposed for the inference methods in the α-GEM family by the effective use of the above-mentioned relations. For the unified platform, a criterion is made clear to uniquely determine the value of a parameter in fuzzy-constraint propagation control for facts given by singletons. Moreover, conditions are derived to make the inference methods in the α-GEM family equivalent to singleton-consequent-type fuzzy inference which has been successfully applied to a wide variety of fields. Thereby, the unified platform can contribute to the construction of an inference engine for both the methods in the α-GEM family and singleton-consequent-type fuzzy inference. Such scheme of the inference engine provides an effective way to make these inference methods transformed into each other in learning for selecting the inference methods as well as for optimizing fuzzy rules.

Fuzzy Inference Based on α-Cuts and Generalized Mean: Relations Between the Methods in its Family and their Unified Platform

Uehara¹,

Hirota²

2017

Noise Reduction with Inference Based on Fuzzy Rule Interpolation at an Infinite Number of Activating Points: Toward Fuzzy Rule Learning in a Unified Inference Platform

Uehara¹,

Hirota²

2018

In order to provide a unified platform for fuzzy inference and fuzzy rule learning with noise-corrupted data, a method is proposed for reducing noise in learning data on the basis of a fuzzy inference method called α-GEMINAS (α-level-set and generalized-mean-based inference with fuzzy rule interpolation at an infinite number of activating points). It is expected to prevent fuzzy rules from overfitting to noise in learning data, especially when there is less learning data available for fuzzy rule optimization. The proposed method is named α-GEMI-ES (α-GEMINAS-based local-evolution toward slight linearity for global smoothness) in this paper. α-GEMI-ES iteratively performs α-GEMINAS and reduces the noise in each iteration. This paper mathematically proves that α-GEMI-ES effectively reduces the noise. The noise-reduction process is decisive and thus relies less on trial-and-error-based progress. The noise is reduced by a large amount in the early iterations and the amount of its reduction is decelerated in the later iterations where the deviation in the learning data is suppressed to a great extent. This property makes it easy to determine the termination conditions for the iterative process. Simulation results demonstrate that α-GEMI-ES properly reduces noise as the mathematical proof suggests. The above-mentioned properties indicate that α-GEMI-ES is feasible in practice for the unified platform.

Noise Reduction with Fuzzy Inference Based on Generalized Mean and Singleton Input–Output Rules: Toward Fuzzy Rule Learning in a Unified Inference Platform

Uehara¹,

Hirota²

2019

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-and-error-based progress. Simulation results demonstrate that noise is properly reduced in each iteration and the deviation in the learning data is suppressed considerably.