TSK-fuzzy modeling based on ε-insensitive learning

Jacek M. Łęski

doi:10.1109/TFUZZ.2004.840094

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TSK-fuzzy modeling based on ε-insensitive learning

2005-04-01

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Jacek M. Łęski

DOI：10.1109/TFUZZ.2004.840094

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Abstract

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In this paper, new learning methods tolerant to imprecision are introduced and applied to fuzzy modeling based on the Takagi-Sugeno-Kang fuzzy system. The fuzzy modeling has an intrinsic inconsistency. It may perform thinking tolerant to imprecision, but learning methods are zero-tolerant to imprecision. The proposed methods make it possible to exclude this intrinsic inconsistency of a fuzzy modeling, where zero-tolerance learning is used to obtain fuzzy model tolerant to imprecision. These new methods can be called E-insensitive learning or e learning, where, in order to fit the fuzzy model to real data, the E-insensitive loss function is used. This leads to a weighted or fuzzified version of Vapnik's support vector regression machine. This paper introduces two approaches to solving the e-insensitive learning problem. The first approach leads to the quadratic programming problem with bound constraints and one linear equality constraint. The second approach leads to a problem of solving a system of linear inequalities. Two computationally efficient numerical methods for the E-insensitive learning are proposed. The E-insensitive learning leads to a model with the minimal Vapnik-Chervonenkis dimension, which results in an improved generalization ability of this model and its outliers robustness. Finally numerical examples are given to demonstrate the validity of the introduced methods.

Keywords:

fuzzy systems

generalization control

robust methods

statistical learning theory

tolerant learning

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