rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Fuzzy Mathematics: Approximation Theory
  name:
    name part: Anastassiou, George A.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2010
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 444 p. 1 illus. online resource.
  abstract: 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: 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 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.
  note: by George A. Anastassiou.
  subject:
    topic: Engineering
  subject:
    topic: Artificial intelligence
  subject:
    topic: Probabilities
  subject:
    topic: Computational intelligence
  subject:
    topic: Engineering
  subject:
    topic: Computational Intelligence
  subject:
    topic: Artificial Intelligence (incl. Robotics)
  subject:
    topic: Probability Theory and Stochastic Processes
  classification: Q342
  classification: 006.3
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Studies in Fuzziness and Soft Computing, 251
  identifier: 9783642112201
  identifier: http://dx.doi.org/10.1007/978-3-642-11220-1
  record info:
    record creation date: 100316
    record change date: 20151204165714.0
    record identifier: 978-3-642-11220-1