Fuzzy Mathematics: Approximation Theory

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Oct 20, 2013 (3 years and 7 months ago)

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Fuzzy Mathematics: Approximation Theory

George A. Anastassiou

This monograph belongs to the broader area of Fuzzy Mathematics and it is the first one in Fuzzy
Approximation Theory. Chapters are self
-
contained with lots of applications and several
advanced
courses

can be taught.
The topics covered are ver
y
diverse. An extensive
background of

Fuzziness and
F
uzzy Real Analysis is given.
The author

cover
s
Fuzzy Differentiati
on and Integration Theory. It follows
about

Fuzzy Ostrowski

i
ne
qualities.
Then are

present
ed

results on classical algebraic and trigonometric
polynomial Fuzzy Ap
proximation. The author

develop
s a complete
theory of convergence with rates of
Fuzzy Positive linear

operators to Fuzzy u
nit operator, the so called Fuzzy Kor
ovkin Th
eory.The related

Fuzzy
Global Smoothness is included. Then follows the study of

Fuzzy Wavelet type operators and their
c
onvergence with rates to Fuzzy u
nit operator
. Similarly are discussed

the Fuzzy Neural Network
Opera
tors. It follows about Fuzzy Rando
m Korovkin
approximation th
eory and
Fuzzy Random Neural
Network approximations.
The author continues with Fuzzy Korovkin approximations in the s
ense of
Summability.

At last are

estimate
d

in the fuzzy sense differences of Fuzzy Wavelet type operators.


The monograph's approach

is quantitative and the
main resul
ts are given via

Fuzzy inequalities,
involving F
uzzy

moduli of continuity, that is F
uzzy Jackson type

inequalities.


The exposed theory is destined and expected to find applications to all aspe
cts of Fuzziness from
theoretical to practical in almost all sciences, technology
, finance

and ind
ustry. Also it has its
interest
with
in

Pure Mathematics. So this monograph is suitable for researchers, graduate students and
seminars of theoretical and appl
ied mathematics, computer science,

statistics and
e
ngineering.