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Fuzzy Mathematics: Approxim...
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
Monografía
monografia Rebiun08275986 https://catalogo.rebiun.org/rebiun/record/Rebiun08275986 cr nn 008mamaa 100316s2010 gw | s |||| 0|eng d 9783642112201 978-3-642-11220-1 10.1007/978-3-642-11220-1 doi UPNA0268826 UPVA 996879776803706 UAM 991007781039004211 UPM 991005575988804212 UCAR 991007918377004213 UR0323771 UPCT u359328 UMO 111015 UYQ bicssc COM004000 bisacsh 006.3 23 Anastassiou, George A. Fuzzy Mathematics: Approximation Theory Recurso electrónico-En línea] by George A. Anastassiou Berlin, Heidelberg Springer Berlin Heidelberg 2010 Berlin, Heidelberg Berlin, Heidelberg Springer Berlin Heidelberg digital Studies in Fuzziness and Soft Computing 1434-9922 251 Engineering (Springer-11647) About 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 Polynomi-Als -- 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 Fuzzywaveletlike 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 In-Equalities -- Fuzzy-Random Neural Network Approximation Operators, Univariate Case- A-Summability and Fuzzy Korovkin Approximation -- A-Summability and Fuzzy Trigonometric Korovkin Approximation -- Uniform Real and Fuzzy Estimates For Distances Betweenwavelet Type Operators At Real and Fuzzy Environment Accesible sólo para usuarios de la UPV Recurso a texto completo 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 Reproducción electrónica Forma de acceso: Web Engineering Artificial intelligence Distribution (Probability theory) Engineering Computational Intelligence Artificial Intelligence (incl. Robotics) Probability Theory and Stochastic Processes SpringerLink (Servicio en línea) Springer eBooks Springer eBooks Printed edition 9783642112195 Studies in Fuzziness and Soft Computing 1434-9922 251