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

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 -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 <-integrable function can be adjusted by changing the subdivision parameters.