Abstract
Universal approximation is the basis of theoretical research and practical application of fuzzy systems. The ability of fuzzy models to model static information has been successfully proven and tested, while on the other hand their limitations in simultaneously modelling dynamical information are well known. Generally, the fuzzy model is a correct zero-order representation of a process or function. However the derivative of its mathematical expression is not necessarily a derivative fuzzy model of the process or function. A perturbed fuzzy system, as a generalization of the traditional fuzzy system, is proposed. It has the ability to uniformly approximate continuous functions and their derivatives on arbitrarily compact sets to the desired degree.
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Salgado, P., Gouveia, F. (2007). Derivative Information from Fuzzy Models. In: Masulli, F., Mitra, S., Pasi, G. (eds) Applications of Fuzzy Sets Theory. WILF 2007. Lecture Notes in Computer Science(), vol 4578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73400-0_8
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DOI: https://doi.org/10.1007/978-3-540-73400-0_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73399-7
Online ISBN: 978-3-540-73400-0
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