Fuzzy Systems with Defuzzification are Universal Approximators - Systems, Man and Cybernetics, Part B, IEEE Transactions on
نویسنده
چکیده
In this paper, we consider a fundamental theoretical question: Is it always possible to design a fuzzy system able of approximating any real continuous function on a compact set with arbitrary accuracy? Moreover, we will research whether the answer to the above question is positive when we restrict to a fixed (but arbitrary) type of fuzzy reasoning and to a subclass of fuzzy relations. This result can be viewed as an existence theorem of an optimal fuzzy system for a wide variety of problems.
منابع مشابه
Fuzzy systems with defuzzification are universal approximators
In this paper, we consider a fundamental theoretical question: Is it always possible to design a fuzzy system capable of approximating any real continuous function on a compact set with arbitrary accuracy? Moreover, we research whether the answer to the above question is positive when we restrict to a fixed (but arbitrary) type of fuzzy reasoning and to a subclass of fuzzy relations. This resul...
متن کاملNecessary conditions on minimal system configuration for general MISO Mamdani fuzzy systems as universal approximators
Recent studies have shown that both Mamdani-type and Takagi-Sugeno-type fuzzy systems are universal approximators in that they can uniformly approximate continuous functions defined on compact domains with arbitrarily high approximation accuracy. In this paper, we investigate necessary conditions for general multiple-input single-output (MISO) Mamdani fuzzy systems as universal approximators wi...
متن کاملHistogram-based fuzzy filter for image restoration
In this paper, we present a novel approach to the restoration of noise-corrupted image, which is particularly effective at removing highly impulsive noise while preserving image details. This is accomplished through a fuzzy smoothing filter constructed from a set of fuzzy membership functions for which the initial parameters are derived in accordance with input histogram. A principle of conserv...
متن کاملOn generating FC3 fuzzy rule systems from data using evolution strategies
Sophisticated fuzzy rule systems are supposed to be flexible, complete, consistent and compact (FC(3)). Flexibility, and consistency are essential for fuzzy systems to exhibit an excellent performance and to have a clear physical meaning, while compactness is crucial when the number of the input variables increases. However, the completeness and consistency conditions are often violated if a fu...
متن کاملComments on Fuzzy Control Systems Design via Fuzzy Lyapunov Functions
This paper considers the work entitled "Fuzzy control systems design via fuzzy Lyapunov functions" and published in IEEE Transactions on Systems, Man, and Cybernetics-Part B , where the authors try to extend the work of Rhee and Won. Nevertheless, the results proposed by Li have been obtained without taking into account a necessary path independency condition to ensure the line integral functio...
متن کامل