This monograph is the Örst in Fuzzy Approximation Theory. It contains
mostly the authorís research work on fuzziness of the last ten years and
relies a lot on [10]-[32] and it is a natural outgrowth of them. It belongs to
the broader area of Fuzzy Mathematics.
Chapters are self-contained and several advanced courses can be taught
out of this book.
We provide lots of applications but always within the framework of Fuzzy
Mathematics. In each chapter is given background and motivations. A complete
list of references is provided at the end. The topics covered are very
diverse. In Chapter 1 we give an extensive basic background on Fuzziness
and Fuzzy Real Analysis, as well a complete description of the book. In the
following Chapters 2,3 we cover in deep Fuzzy Di§erentiation and Integration
Theory, e.g. we present Fuzzy Taylor Formulae. It follows Chapter 4
on Fuzzy Ostrowski Inequalities. Then in Chapters 5, 6 we present results
on classical algebraic and trigonometric polynomial Fuzzy Approximation.
In Chapters 7-11 we develop completely the theory of convergence with
rates of Fuzzy Positive linear operators to Fuzzy Unit operator, the so
called Fuzzy Korovkin Theory. We include there the related topic of Fuzzy
Global Smoothness, see Chapter 9. In Chapters 12-14 we deal with Fuzzy
Wavelet type operators and their convergence with rates to Fuzzy Unit operator.
In Chapters 15-16 we discuss similarly as above the Fuzzy Neural
Network Operators. In Chapter 17 we deal with Fuzzy Random Korovkin
type approximation theory. In Chapter 18 we deal with Fuzzy Random
Neural Network approximations.