Studies in Systems, Decision and Control

Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators

Authors: Anastassiou, George A.

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  • Presents a range of original approaches to approximation
  • All chapters are self-contained and can be read independently
  • Provides a deeper formal analysis of several issues that are relevant to decision making, complex processes, systems modeling and control, and related areas  
  • Is suitable as a textbook for related graduate classes
  • Obtains results that are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional)
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eBook $129.00
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  • ISBN 978-3-030-04287-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-3-030-04286-8
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  • Usually dispatched within 3 to 5 business days.
About this book

Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory. These integrals are only subadditive and only the first two are positive linear, and they produce very fast and flexible approximations based on limited data. The author presents both the univariate and multivariate cases. The involved set functions are much weaker forms of the Lebesgue measure and they were conceived to fulfill the needs of economic theory and other applied sciences.

The approaches presented here are original, and all chapters are self-contained and can be read independently. Moreover, the book’s findings are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional). Accordingly, it offers a unique resource for researchers, graduate students, and for coursework in the above-mentioned fields, and belongs in all science and engineering libraries.

Table of contents (17 chapters)

Table of contents (17 chapters)
  • Approximation with Rates by Kantorovich–Choquet Quasi-interpolation Neural Network Operators

    Anastassiou, George A.

    Pages 1-21

  • Approximation with Rates by Perturbed Kantorovich–Choquet Neural Network Operators

    Anastassiou, George A.

    Pages 23-54

  • Approximation with Rates by Shift Invariant Univariate Sublinear-Choquet Operators

    Anastassiou, George A.

    Pages 55-72

  • Approximation with Rates by Shift Invariant Multivariate Sublinear-Choquet Operators

    Anastassiou, George A.

    Pages 73-91

  • Hardy Type Inequalities for Choquet Integrals

    Anastassiou, George A.

    Pages 93-108

Buy this book

eBook $129.00
price for USA in USD (gross)
  • ISBN 978-3-030-04287-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-3-030-04286-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators
Authors
Series Title
Studies in Systems, Decision and Control
Series Volume
190
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-04287-5
DOI
10.1007/978-3-030-04287-5
Hardcover ISBN
978-3-030-04286-8
Series ISSN
2198-4182
Edition Number
1
Number of Pages
XIV, 347
Number of Illustrations
1 b/w illustrations
Topics