Multivariate Fuzzy Perturbed Neural Network Operators Approximation
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Authors
George A. Anastassiou
- Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.
Abstract
This article studies the determination of the rate of convergence to the unit of each of three newly introduced
here multivariate fuzzy perturbed normalized neural network operators of one hidden layer. These are given
through the multivariate fuzzy modulus of continuity of the involved multivariate fuzzy number valued
function or its high order fuzzy partial derivatives and that appears in the right-hand side of the associated
fuzzy multivariate Jackson type inequalities. The multivariate activation function is very general, especially
it can derive from any sigmoid or bell-shaped function. The right hand sides of our multivariate fuzzy
convergence inequalities do not depend on the activation function. The sample multivariate fuzzy functionals
are of Stancu, Kantorovich and Quadrature types. We give applications for the first fuzzy partial derivatives
of the involved function.
Share and Cite
ISRP Style
George A. Anastassiou, Multivariate Fuzzy Perturbed Neural Network Operators Approximation, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 6, 383--406
AMA Style
Anastassiou George A., Multivariate Fuzzy Perturbed Neural Network Operators Approximation. J. Nonlinear Sci. Appl. (2014); 7(6):383--406
Chicago/Turabian Style
Anastassiou, George A.. "Multivariate Fuzzy Perturbed Neural Network Operators Approximation." Journal of Nonlinear Sciences and Applications, 7, no. 6 (2014): 383--406
Keywords
- Multivariate neural network fuzzy approximation
- fuzzy partial derivative
- multivariate fuzzy modulus of continuity
- multivariate fuzzy operator.
MSC
- 26E50
- 41A17
- 41A25
- 41A36
- 47S40
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