- Introductory book to fuzzy mathematics
- Presents the state of the art of approximation theory and fuzzy mathematics
Buy this book
- 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
Pages 1-14
-
ABOUT H-FUZZY DIFFERENTIATION
Pages 15-50
-
ON FUZZY TAYLOR FORMULAE
Pages 51-63
-
FUZZY OSTROWSKI INEQUALITIES
Pages 65-73
-
A FUZZY TRIGONOMETRIC APPROXIMATION THEOREM OF WEIERSTRASS-TYPE
Pages 75-82
-
Table of contents (21 chapters)
Recommended for you
Bibliographic Information
- Bibliographic Information
-
- Book Title
- Fuzzy Mathematics: Approximation Theory
- Authors
-
- George A. Anastassiou
- 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
- 1 b/w illustrations
- Topics
