000 04458nam a22004695i 4500
001 978-3-642-11220-1
003 DE-He213
005 20140220084530.0
007 cr nn 008mamaa
008 100316s2010 gw | s |||| 0|eng d
020 _a9783642112201
_9978-3-642-11220-1
024 7 _a10.1007/978-3-642-11220-1
_2doi
050 4 _aQ342
072 7 _aUYQ
_2bicssc
072 7 _aCOM004000
_2bisacsh
082 0 4 _a006.3
_223
100 1 _aAnastassiou, George A.
_eauthor.
245 1 0 _aFuzzy Mathematics: Approximation Theory
_h[electronic resource] /
_cby George A. Anastassiou.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aStudies in Fuzziness and Soft Computing,
_x1434-9922 ;
_v251
505 0 _aABOUT H-FUZZY DIFFERENTIATION -- ON FUZZY TAYLOR FORMULAE -- FUZZY OSTROWSKI INEQUALITIES -- A FUZZY TRIGONOMETRIC APPROXIMATION THEOREM OF WEIERSTRASS-TYPE -- ON BEST APPROXIMATION AND JACKSON-TYPE ESTIMATES BY GENERALIZED FUZZY POLYNOMIALS -- BASIC FUZZY KOROVKIN THEORY -- FUZZY TRIGONOMETRIC KOROVKIN THEORY -- FUZZY GLOBAL SMOOTHNESS PRESERVATION -- FUZZY KOROVKIN THEORY AND INEQUALITIES -- HIGHER ORDER FUZZY KOROVKIN THEORY USING INEQUALITIES -- FUZZY WAVELET LIKE OPERATORS -- ESTIMATES TO DISTANCES BETWEEN FUZZY WAVELET LIKE OPERATORS -- FUZZY APPROXIMATION BY FUZZY CONVOLUTION OPERATORS -- DEGREE OF APPROXIMATION OF FUZZY NEURAL NETWORK OPERATORS, UNIVARIATE CASE -- HIGHER DEGREE OF FUZZY APPROXIMATION BY FUZZY WAVELET TYPE AND NEURAL NETWORK OPERATORS -- FUZZY RANDOM KOROVKIN THEOREMS AND INEQUALITIES -- FUZZY-RANDOM NEURAL NETWORK APPROXIMATION OPERATORS, UNIVARIATE CASE -- -SUMMABILITY AND FUZZY KOROVKIN APPROXIMATION -- -SUMMABILITY AND FUZZY TRIGONOMETRIC KOROVKIN APPROXIMATION -- UNIFORM REAL AND FUZZY ESTIMATES FOR DISTANCES BETWEEN WAVELET TYPE OPERATORS AT REAL AND FUZZY ENVIRONMENT.
520 _aThis 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.
650 0 _aEngineering.
650 0 _aArtificial intelligence.
650 0 _aDistribution (Probability theory).
650 1 4 _aEngineering.
650 2 4 _aComputational Intelligence.
650 2 4 _aArtificial Intelligence (incl. Robotics).
650 2 4 _aProbability Theory and Stochastic Processes.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642112195
830 0 _aStudies in Fuzziness and Soft Computing,
_x1434-9922 ;
_v251
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-11220-1
912 _aZDB-2-ENG
999 _c111814
_d111814