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This monograph is the continuation and completion of the monograph, "Intelligent Systems: Approximation by Artificial Neural Networks" written by the same author and published 2011 by Springer.

The book you hold in hand presents the complete recent and original work of the author in approximation by neural networks. Chapters are written in a self-contained style and can be read independently. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The book´s results are expected to find applications in many areas of applied mathematics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science and engineering libraries.

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Rate of Convergence of Basic Neural Network Operators to the Unit.- Rate of Convergence of Basic Multivariate Neural Network Operators.- Fractional Neural Network Operators Approximation.- Fractional Approximation Using Cardaliaguet-Euvrard Neural Networks.- Fractional Asymptotic Expansions for Quasi-interpolation neural Networks.- Voronovskaya Type Asymptotic Expansions for Multivariate Neural Networks.- Fractional Approximation by Bell and Squashing Neural Networks.- Fractional Asymptotic Expansions For Bell And Squashing Neural Networks.- Multivariate Asymptotic Expansions for Bell and Squashing Neural Networks.- Multivariate Fuzzy-Random Normalized Neural Network Approximation.- Fuzzy Fractional Approximations by Fuzzy Bell and Squashing Neural Networks.- Fuzzy Fractional Neural Network Approximation.- Multivariate Fuzzy Approximation Using Basic Neural Network Operators.- Multivariate Fuzzy Approximation Using Quasi-Interpolation Neural Networks.- Multivariate Fuzzy-Random Neural Networks Approximation.- Approximation by Kantorovich and Quadrature type neural Networks.- Univariate Error Function Based Neural Network Approximations.- Multivariate Error Function Based Neural Network Operators Approximation.- Asymptotic Expansions for Error Function Based Neural Networks.- Fuzzy Fractional Error Function Relied Neural Network Approximations.- Multivariate Fuzzy Approximation by Neural Networks.- Fuzzy-Random Error Function Relied Neural Network Approximations.- Approximation by Perturbed Neural Networks.- Approximations by Multivariate Perturbed Neural Networks.- Voronovskaya type Asymptotic Expansions for Perturbed Neural Networks.- Approximation using Fuzzy Perturbed Neural Networks.- Multivariate Fuzzy Perturbed Neural Network Approximations.- Multivariate Fuzzy-Random Perturbed Neural Network Approximations.

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"The present book ... contains mainly the research results of the author in recent years. ... To each chapter references are added. ... The formal presentation by Springer is excellent." (Claudia Simionescu-Badea, zbMATH, Vol. 1325.68008, 2016)

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