A Takagi-Sugeno model with fuzzy inputs viewed from multidimensional interval analysis

摘要

Takagi-Sugeno (T-S) fuzzy systems have been successfully applied to a wide range of problems and have demonstrated significant advantages in nonlinear control. This paper presents a fuzzified T-S interpolation-approximation system mainly based on the specification of a multidimensional crisp partition that defines the corresponding local regions (multidimensional intervals) where the corresponding rules apply, the related output functions and a reduced set of global fuzzy parameters. These fuzzy parameters capture the different uncertainties of a fuzzy system: imprecision of inputs, vagueness of antecedent linguistic labels and smoothness requirements of outputs. This approach makes easier the design of a zero-order product-sum T-S system with fuzzified inputs, fuzzified antecedent crisp partition, and outputs with an additional spatial output filter. Convolution operations applied on an equalized and normalized input domain are considered to specify the corresponding fuzzification of a crisp partition. The kernels of these convolutions are even B-spline functions of order n, constructed from a n-fold convolution of an even interval characteristic function. We use a correctness-preserving transformation to simplify the output computation: a global transformation of imprecision of inputs, vagueness of antecedent terms and smoothness requirements of outputs into a set of off-line convolution operations applied to the corresponding antecedent crisp partition. By this method a fuzzified zero-order T-S system defined on a multidimensional crisp partition is directly transformed into a multidimensional spline interpolator-approximator by means of fuzzy operations and an equalization-normalization of the corresponding input domain.