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TSK-fuzzy modeling based on ϵ-insensitive learning

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1 Author(s)
Leski, J.M. ; Div. of Biomed. Electron., Silesian Univ. of Technol., Gliwice, Poland

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 ε-insensitive learning or ε learning, where, in order to fit the fuzzy model to real data, the ε-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 ε-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 ε-insensitive learning are proposed. The ε-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.

Published in:

Fuzzy Systems, IEEE Transactions on  (Volume:13 ,  Issue: 2 )