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Fuzzy Mathematics: Approximation Theory

  • George A. Anastassiou

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 251)

Table of contents

  1. Front Matter
  2. George A. Anastassiou
    Pages 1-14
  3. George A. Anastassiou
    Pages 15-50
  4. George A. Anastassiou
    Pages 51-63
  5. George A. Anastassiou
    Pages 65-73
  6. George A. Anastassiou
    Pages 99-104
  7. George A. Anastassiou
    Pages 105-113
  8. George A. Anastassiou
    Pages 115-124
  9. George A. Anastassiou
    Pages 125-157
  10. George A. Anastassiou
    Pages 159-190
  11. George A. Anastassiou
    Pages 191-207
  12. George A. Anastassiou
    Pages 237-261
  13. George A. Anastassiou
    Pages 309-345
  14. Back Matter

About this book

Introduction

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.

Keywords

approximation theory artificial intelligence computer-assisted surgery fuzziness fuzzy mathematics mathematics statistics

Authors and affiliations

  • George A. Anastassiou
    • 1
  1. 1.Department of Mathematical SciencesThe University of Memphis38152USA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-11220-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-11219-5
  • Online ISBN 978-3-642-11220-1
  • Series Print ISSN 1434-9922
  • Series Online ISSN 1860-0808
  • Buy this book on publisher's site
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