Max-Product Shepard Approximation Operators
Barnabás Bede*, Hajime Nobuhara**, János Fodor***,
and Kaoru Hirota**
*Department of Mechanical and System Engineering, Bánki Donát Faculty of Mechanical Engineering, Budapest Tech, Népszinház u. 8, H-1081 Budapest, Hungary
**Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midoriku, Yokohama 226-8502, Japan
***Institute of Intelligent Engineering Systems, John von Neumann Faculty of Informatics, Budapest Tech, Bécsi út 96/b, H-1034 Budapest, Hungary
-  G. A. Anastassiou, “Rate of convergence of fuzzy neural network operators, univariate case,” J. Fuzzy Math. Vol.10, No.3, pp. 755-780, 2002.
-  G. A. Anastassiou, and S. G. Gal, “Approximation Theory: Moduli of Continuity and Global Smoothness Preservation,” Birkhäuser, Boston-Basel-Berlin, 2000.
-  R. A. Devore, and G. G. Lorentz, “Constructive Approximation, Polynomials and Splines Approximation,” Springer-Verlag, Berlin, Heidelberg, 1993.
-  A. DiNola, S. Sessa, W. Pedrycz, and E. Sanchez, “Fuzzy Relation Equation and Their Applications to Knowledge Engineering,” Kluwer Academic Publishers, 1989.
-  G. Ferrari-Trecate, and R. Rovatti, “Fuzzy systems with overlapping Gaussian concepts: Approximation properties in Sobolev norms,” Fuzzy Sets and Systems, 130, pp. 137-145, 2002.
-  L. Horváth, and I. J. Rudas, “Modeling and Problem Solving Methods for Engineers,” ISBN 0-12-602250-X, Elsevier, Academic Press, 2004.
-  L. T. Kóczy, and K. Hirota, “Approximate reasoning by linear rule interpolation and general approximation,” International Journal of Approximate Reasoning, 9, pp. 197-225, 1993.
-  P. Liu, “Universal approximations of continuous fuzzy-valued functions by multi-layer regular fuzzy neural networks,” Fuzzy Sets and Systems, 119, pp. 313-320, 2001.
-  E. H. Mamdani, and S. Assilian, “An experiment in linguistic synthesis with a fuzzy logic controller,” J. Man Machine Stud., 7, pp. 1-13, 1975.
-  E. Pap, and K. Jegdić, “Pseudo-analysis and its application in railway rooting,” Fuzzy Sets and Systems, 116, pp. 103-118, 2000.
-  J. Szabados, “On a problem of R. DeVore,” Acta Math. Hungar., 27(1-2), pp. 219-223, 1976.
-  D. Tikk, “Notes on the approximation rate of fuzzy KH interpolators,” Fuzzy Sets and Systems, 138, pp. 441-453, 2003.
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