A Takagi–Sugeno model with fuzzy inputs viewed from multidimensional interval analysis
✍ Scribed by Felipe Fernández; Julio Gutiérrez
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 965 KB
- Volume
- 135
- Category
- Article
- ISSN
- 0165-0114
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✦ Synopsis
Takagi-Sugeno (T-S) fuzzy systems have been successfully applied to a wide range of problems and have demonstrated signiÿcant advantages in nonlinear control. This paper presents a fuzziÿed T-S interpolationapproximation system mainly based on the speciÿcation of a multidimensional crisp partition that deÿnes 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 di erent 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 fuzziÿed inputs, fuzziÿed antecedent crisp partition, and outputs with an additional spatial output ÿlter. Convolution operations applied on an equalized and normalized input domain are considered to specify the corresponding fuzziÿcation 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 o -line convolution operations applied to the corresponding antecedent crisp partition. By this method a fuzziÿed zero-order T-S system deÿned 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.