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Statistical Modeling, Analysis and Management of Fuzzy Data

  • Book
  • © 2002

Overview

Editors:
  1. Carlo Bertoluzza

    1. Dipartimento di Informatica e Sistemistica, Università degli Studi di Pavia, Pavia, Italy

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  2. María-Ángeles Gil

    1. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Oviedo, Spain

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  3. Dan A. Ralescu

    1. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA

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  • States the complementary rather than competitive relationship between Probability and Fuzzy Set Theory
  • Allows solutions to reallife problems with suitable combinations of both theories
  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 87)

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Table of contents (18 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Fuzziness and Randomness

    1. Front Matter

      Pages 1-1
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    2. Fuzziness and randomness

      • Irwin R. Goodman, Hung T. Nguyen
      Pages 3-21

  3. Fuzzy-Valued Random Elements

    1. Front Matter

      Pages 23-23
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    2. On the variance of random fuzzy variables

      • Ralf Körner, Wolfgang Näther
      Pages 25-42

    3. f-inequality indices for fuzzy random variables

      • María Asunción Lubiano, María Ángeles Gil
      Pages 43-63

    4. Traditional techniques to prove some limit theorems for fuzzy random variables

      • Ana Colubi
      Pages 64-71

    5. Convergence in graph for fuzzy valued martingales and smartingales

      • Shoumei Li, Yukio Ogura
      Pages 72-89

    6. Remarks on Korovkin-type approximation of fuzzy random variables

      • Pedro Terán, Miguel López-Díaz
      Pages 90-103

    7. Several notions of differentiability for fuzzy set-valued mappings

      • Luis J. Rodríguez-Muñiz
      Pages 104-116

  4. Possibility, Probability and Fuzzy Measures

    1. Front Matter

      Pages 117-117
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    2. Average level of a fuzzy set

      • Dan A. Ralescu
      Pages 119-126

    3. Second order possibility measure induced by a fuzzy random variable

      • Inés Couso, Susana Montes, Pedro Gil
      Pages 127-144

    4. Measure extension from meet-systems and falling measures representation

      • P. Z. Wang, Y. C. Chen, B. T. Low
      Pages 145-159

    5. The structure of fuzzy measure families induced by upper and lower probabilities

      • Andrew G. Bronevich, Alexander N. Karkishchenko
      Pages 160-172

    6. Statistical classes and fuzzy set theoretical classification of probability distributions

      • Andrew G. Bronevich, Alexander N. Karkishchenko
      Pages 173-195

  5. Statistics and Fuzzy Data Analysis

    1. Front Matter

      Pages 197-197
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    2. Statistics with one-dimensional fuzzy data

      • Reinhard Viertl
      Pages 199-212

    3. Testing fuzzy hypotheses with vague data

      • Przemysław Grzegorzewski
      Pages 213-225

    4. Possibilistic interpretation of fuzzy statistical tests

      • Olgierd Hryniewicz
      Pages 226-238
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Keywords

About this book

"Statistical Modeling, Analysis and Management of Fuzzy Data," or SMFD for short, is an important contribution to a better understanding of a basic issue -an issue which has been controversial, and still is though to a lesser degree. In substance, the issue is: are fuzziness and randomness distinct or coextensive facets of uncertainty? Are the theories of fuzziness and random­ ness competitive or complementary? In SMFD, these and related issues are addressed with rigor, authority and insight by prominent contributors drawn, in the main, from probability theory, fuzzy set theory and data analysis com­ munities. First, a historical perspective. The almost simultaneous births -close to half a century ago-of statistically-based information theory and cybernetics were two major events which marked the beginning of the steep ascent of probability theory and statistics in visibility, influence and importance. I was a student when information theory and cybernetics were born, and what is etched in my memory are the fascinating lectures by Shannon and Wiener in which they sketched their visions of the coming era of machine intelligence and automation of reasoning and decision processes. What I heard in those lectures inspired one of my first papers (1950) "An Extension of Wiener's Theory of Prediction," and led to my life-long interest in probability theory and its applications to information processing, decision analysis and control.

Editors and Affiliations

  • Dipartimento di Informatica e Sistemistica, Università degli Studi di Pavia, Pavia, Italy

    Carlo Bertoluzza

  • Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Oviedo, Spain

    María-Ángeles Gil

  • Department of Mathematical Sciences, University of Cincinnati, Cincinnati, USA

    Dan A. Ralescu

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