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Banach Space Valued Neural Network: Ordinary and Fractional Approximation and Interpolation
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Banach Space Valued Neural Network: Ordinary and Fractional Approximation and InterpolationНазвание: Banach Space Valued Neural Network
Автор: George A. Anastassiou
Издательство: Springer
Серия: Studies in Computational Intelligence
Год: 2023
Страниц: 429
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

This book is about the generalization and modernization of approximation by neural network operators. Functions under approximation and the neural networks are Banach space valued. These are induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian, and generalized symmetric sigmoid functions. Ordinary, fractional, fuzzy, and stochastic approximations are exhibited at the univariate, fractional, and multivariate levels. Iterated-sequential approximations are also covered. The book’s results are expected to find applications in the many areas of applied mathematics, Computer Science and engineering, especially in Artificial Intelligence (AI) and Machine Learning (ML). Other possible applications can be in applied sciences like statistics, economics, etc. Therefore, this book is suitable for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.

The innovation here is that the neural networks are Banach space valued, induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian and generalized symmetric sigmoid functions. Thus, in this monograph, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. We exhibit univariate, fractional and multivariate approximations. Iterated-sequential approximations are also studied. The new and important feature here is that the functions under approximation are Banach space valued.

As a result, this monograph is the natural and expected evolution of recent author’s research work put in a book form for the first time. The presented approaches are original, and the chapters are self-contained and can be read independently. Thismonograph is suitable to be used in related graduate classes and research projects.

Here we study the univariate fuzzy fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation arctangent-algebraic-Gudermannian-generalized symmetrical activation function relied fuzzy neural network operators. These approximations are derived by establishing fuzzy Jackson type inequalities involving the fuzzy moduli of continuity of the right and left Caputo fuzzy fractional derivatives of the involved function. The approximations are fuzzy pointwise and fuzzy uniform. The related feed-forward fuzzy neural networks are with one hidden layer. We study also the fuzzy integer derivative and just fuzzy continuous cases. Our fuzzy fractional approximation result using higher order fuzzy differentiation converges better than in the fuzzy just continuous case.

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