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Notes on the approximation rate of fuzzy KH interpolators

机译：关于模糊KH插值器的逼近率的注意事项

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摘要

This paper investigates the approximation behaviour of the Koczy-Hirota (KH) interpolative fuzzy controllers. First, in accordance with the remarks in (Fuzzy Sets and Systems 125(1) (2002) 105), it is pointed out that it is a fuzzy generalization of the Shepard operator. Shepard operator has thoroughly studied by approximation theorist since the mid-1970s. Exploiting the aforementioned relationship, we establish analog results on the approximation rate of KH controllers. The optimal order and class of approximation (saturation problem) are determined for certain values of the exponent A. Corresponding results on the modified alpha-cut based interpolation method, being an improvement of the KH interpolator, are also provided. The results offer trade-off facilities between approximation accuracy and the number of rules. As a consequence, the necessary and sufficient number of rules can be determined for a prescribed accuracy.
机译：本文研究了Koczy-Hirota（KH）插值模糊控制器的逼近行为。首先，根据（Fuzzy Sets and Systems 125（1）（2002）105）中的论述，指出这是Shepard算子的模糊概括。从1970年代中期开始，Shepard算子就已经由近似理论家进行了深入研究。利用上述关系，我们建立了关于KH控制器近似率的模拟结果。确定指数A的某些值的最佳近似阶数和类别（饱和问题）。还提供了对改进的基于alpha割的插值方法（作为KH插值器的改进）的相应结果。结果提供了近似精度和规则数量之间的折衷工具。因此，可以为规定的准确性确定必要和足够数量的规则。

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