Multilayer feedforward networks are universal approximators
Neural Networks
Approximation theory and feedforward networks
Neural Networks
Ordering, distance and closeness of fuzzy sets
Fuzzy Sets and Systems - Special issue on fuzzy data analysis
Fuzzy Systems as Universal Approximators
IEEE Transactions on Computers
Fuzzy systems and approximation
Fuzzy Sets and Systems - Special issue on methods for data analysis in classificatin and control
Stability of interpolative fuzzy KH controllers
Fuzzy Sets and Systems - Fuzzy control
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Comprehensive analysis of a new fuzzy rule interpolation method
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Mixed H 2/H∞ autopilot design of bank-to-turn missiles using fuzzy basis function networks
Fuzzy Sets and Systems
Kernel shapes of fuzzy sets in fuzzy systems for function approximation
Information Sciences: an International Journal
Approximation by pseudo-linear operators
Fuzzy Sets and Systems
Approximation by Shepard type pseudo-linear operators and applications to Image Processing
International Journal of Approximate Reasoning
Fuzzy spline interpolation with optimal property in parametric form
Information Sciences: an International Journal
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This paper investigates the approximation behaviour of the Kóczy-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 λ. 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.