Approximation properties of piece-wise parabolic functions fuzzy logic systems

  • Authors:

  • Radhia Hassine;Fakhreddine Karray;Adel M. Alimi;Mohamed Selmi

  • Affiliations:

  • Department of Mathematics, Faculty of Sciences of Monastir, Boulevard de l'environnement---Monastir 5000---Tunisia;PAMI: Pattern Analysis and Machine Intelligence Laboratory, Systems Design Engineering Department, University of Waterloo, Waterloo, Canada, ON N2L 3G1;REGIM: REsearch Group on Intelligent Machines, Department of Electrical Engineering, University of Sfax, ENIS, BP W, Sfax 3038, Tunisia;Laboratory of Physics and Mathematics, Department of Mathematics, Faculty of Sciences of Monastir---Monastir 5000---Tunisia

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2006

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Abstract

Spline functions are widely used in the field of approximation theory and its applications. In this article, we propose the use of @p functions which are spline functions of degree two, as membership functions of the input variables. At first, we show by a constructive theory that multi-input-single-output (MISO) Sugeno Fuzzy Logic Systems with @p input variables membership functions are universal approximators to every continuously differentiable function defined on a compact subset of R^n. Moreover they are of first order approximation accuracy. Then, we show that with appropriately chosen parameters of the @p functions, fuzzy logic systems with @p input variables membership functions are universal approximators not only for the function itself but also for its first order derivative.