Studies in Fuzziness and Soft Computing

Fuzzy Mathematics: Approximation Theory

Authors: Anastassiou, George A.

  • Introductory book to fuzzy mathematics
  • Presents the state of the art of approximation theory and fuzzy mathematics
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eBook $189.00
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valid through November 5, 2017
  • ISBN 978-3-642-11220-1
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  • Included format: PDF
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Hardcover $249.00
price for USA
valid through November 5, 2017
  • ISBN 978-3-642-11219-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $249.00
price for USA
valid through November 5, 2017
  • ISBN 978-3-642-26239-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

This monograph belongs to the broader area of Fuzzy Mathematics and it is the first one in Fuzzy Approximation Theory. The chapters are self-contained with lots of applications to teach several advanced courses and the topics covered are very diverse. An extensive background of Fuzziness and Fuzzy Real Analysis is given. The author covers Fuzzy Differentiation and Integration Theory followed by Fuzzy Ostrowski inequalities. Then results on classical algebraic and trigonometric polynomial Fuzzy Approximation are presented. The author develops a complete theory of convergence with rates of Fuzzy Positive linear operators to Fuzzy unit operator, the so-called Fuzzy Korovkin Theory. The related Fuzzy Global Smoothness is included. Then follows the study of Fuzzy Wavelet type operators and their convergence with rates to Fuzzy unit operator. Similarly the Fuzzy Neural Network Operators are discussed followed by Fuzzy Random Korovkin approximation theory and Fuzzy Random Neural Network approximations. The author continues with Fuzzy Korovkin approximations in the sense of Summability. Finally fuzzy sense differences of Fuzzy Wavelet type operators are estimated.

The monograph's approach is quantitative and the main results are given via Fuzzy inequalities, involving Fuzzy moduli of continuity, that is Fuzzy Jackson type inequalities.

The exposed theory is destined and expected to find applications to all aspects of Fuzziness from theoretical to practical in almost all sciences, technology, finance and industry. Also it has its interest within Pure Mathematics. So this monograph is suitable for researchers, graduate students and seminars of theoretical and applied mathematics, computer science, statistics and engineering.

Table of contents (21 chapters)

  • INTRODUCTION

    Anastassiou, George A.

    Pages 1-14

  • ABOUT H-FUZZY DIFFERENTIATION

    Anastassiou, George A.

    Pages 15-50

  • ON FUZZY TAYLOR FORMULAE

    Anastassiou, George A.

    Pages 51-63

  • FUZZY OSTROWSKI INEQUALITIES

    Anastassiou, George A.

    Pages 65-73

  • A FUZZY TRIGONOMETRIC APPROXIMATION THEOREM OF WEIERSTRASS-TYPE

    Anastassiou, George A.

    Pages 75-82

Buy this book

eBook $189.00
price for USA (gross)
valid through November 5, 2017
  • ISBN 978-3-642-11220-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $249.00
price for USA
valid through November 5, 2017
  • ISBN 978-3-642-11219-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $249.00
price for USA
valid through November 5, 2017
  • ISBN 978-3-642-26239-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fuzzy Mathematics: Approximation Theory
Authors
Series Title
Studies in Fuzziness and Soft Computing
Series Volume
251
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-11220-1
DOI
10.1007/978-3-642-11220-1
Hardcover ISBN
978-3-642-11219-5
Softcover ISBN
978-3-642-26239-5
Series ISSN
1434-9922
Edition Number
1
Number of Pages
XII, 444
Number of Illustrations and Tables
1 b/w illustrations
Topics