Geodesic
Multivariate Fuzzy Perturbed Neural Network Operators Approximation
Anastassiou, George A.1
1 Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A
Journal of nonlinear sciences and its applications, Tome 7 (2014) no. 6, p. 383-406.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.007.06.03
Classification : 26E50, 41A17, 41A25, 41A36, 47S40
Keywords: Multivariate neural network fuzzy approximation, fuzzy partial derivative, multivariate fuzzy modulus of continuity, multivariate fuzzy operator.

Anastassiou, George A. 1

1 Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A 
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Anastassiou, George A. Multivariate Fuzzy Perturbed Neural Network Operators Approximation. Journal of nonlinear sciences and its applications, Tome 7 (2014) no. 6, p. 383-406. doi : 10.22436/jnsa.007.06.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.007.06.03/

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