Intelligent Systems II: Complete Approximation by Neural Network Operators

✍ Scribed by George A. Anastassiou (auth.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 712
• Series: Studies in Computational Intelligence 608
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xv
Rate of Convergence of Basic Neural Network Operators to the Unit-Univariate Case....Pages 1-9
Rate of Convergence of Basic Multivariate Neural Network Operators to the Unit....Pages 11-21
Fractional Neural Network Operators Approximation....Pages 23-58
Fractional Approximation Using Cardaliaguet-Euvrard and Squashing Neural Networks....Pages 59-87
Fractional Voronovskaya Type Asymptotic Expansions for Quasi-interpolation Neural Networks....Pages 89-101
Voronovskaya Type Asymptotic Expansions for Multivariate Quasi-interpolation Neural Networks....Pages 103-118
Fractional Approximation by Normalized Bell and Squashing Type Neural Networks....Pages 119-141
Fractional Voronovskaya Type Asymptotic Expansions for Bell and Squashing Type Neural Networks....Pages 143-152
Multivariate Voronovskaya Type Asymptotic Expansions for Normalized Bell and Squashing Type Neural Networks....Pages 153-163
Multivariate Fuzzy-Random Normalized Neural Network Approximation....Pages 165-191
Fuzzy Fractional Approximations by Fuzzy Normalized Bell and Squashing Type Neural Networks....Pages 193-214
Fuzzy Fractional Neural Network Approximation Using Fuzzy Quasi-interpolation Operators....Pages 215-249
Higher Order Multivariate Fuzzy Approximation Using Basic Neural Network Operators....Pages 251-266
High Order Multivariate Fuzzy Approximation Using Quasi-interpolation Neural Networks....Pages 267-297
Multivariate Fuzzy-Random Quasi-interpolation Neural Networks Approximation....Pages 299-320
Approximation by Kantorovich and Quadrature Type Quasi-interpolation Neural Networks....Pages 321-330
Univariate Error Function Based Neural Network Approximations....Pages 331-373
Multivariate Error Function Based Neural Network Operators Approximation....Pages 375-407
Voronovskaya Type Asymptotic Expansions for Error Function Based Quasi-interpolation Neural Networks....Pages 409-430
Fuzzy Fractional Error Function Relied Neural Network Approximations....Pages 431-463
High Degree Multivariate Fuzzy Approximation by Neural Network Operators Using the Error Function....Pages 465-496
Multivariate Fuzzy-Random Error Function Relied Neural Network Approximations....Pages 497-521
Approximation by Perturbed Neural Networks....Pages 523-551
Approximations by Multivariate Perturbed Neural Networks....Pages 553-585
Voronovskaya Type Asymptotic Expansions for Perturbed Neural Networks....Pages 587-626
Approximation Using Fuzzy Perturbed Neural Networks....Pages 627-654
Multivariate Fuzzy Perturbed Neural Network Approximations....Pages 655-686
Multivariate Fuzzy-Random Perturbed Neural Network Approximations....Pages 687-710
Back Matter....Pages 711-712

✦ Subjects

Computational Intelligence; Artificial Intelligence (incl. Robotics)