# Matching localization algorithm of nonlinear T–S fuzzy system constructed by the piecewise linear function

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## Abstract

The piecewise linear function is a generalization of a segmentation linear functions with one variable in the multivariate case, which is an important tool to describe the relationships between fuzzy system and approximation function. Firstly, aiming at the \({\hat{\mu }}\)-integrable function, the concrete method of constructing piecewise linear functions and their analytical expressions were introduced, furthermore, based on the piecewise linear functions, we constructed the nonlinear T–S fuzzy systems with a singleton fuzzifier in this paper. And then, we put forward the matching-localization algorithm of the fuzzy system based on the spatial positioning mode for the input variables in the domain. Finally, the effectiveness of the matching localization algorithm of the nonlinear T–S fuzzy system was verified by the means of the simulation example. The results show that the approximating ability of the fuzzy system to a \({\hat{\mu }}\)-integrable function can be adjusted by changing the subdivision parameters.

## Keywords

Piecewise linear function Singleton fuzzifier Nonlinear T–S fuzzy system \({\hat{\mu }}\)-integrable function Matching-localization algorithm## Notes

### Acknowledgements

This work has been supported by National Natural Science Foundation China (Grant no. 61374009).

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