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Soft Methods in Probability, Statistics and Data Analysis

  • Conference proceedings
  • © 2002

Overview

Editors:
  1. Przemysław Grzegorzewski

    1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

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  2. Olgierd Hryniewicz

    1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

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  3. María Ángeles Gil

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

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Part of the book series: Advances in Intelligent and Soft Computing (AINSC, volume 16)

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Table of contents (38 papers)

  1. Front Matter

    Pages I-X
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  3. Soft Methods in Probability: Fundamentals

    1. Front Matter

      Pages 63-63
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    2. Independence and Conditioning in a Connectivistic Fuzzy Logic Framework

      • Joseph Aguilar-Martin
      Pages 65-75

    3. About Ideals on the Set of Fuzzy Measures

      • Andrew G. Bronevich, Alexander N. Karkishchenko
      Pages 76-83

    4. Operators for Convolution of Fuzzy Measures

      • Andrew G. Bronevich, Alexander E. Lepskiy
      Pages 84-91

    5. Probabilities of Fuzzy Events Based on Scalar Cardinalities

      • Jaume Casasnovas, Francesc Rosselló
      Pages 92-97

    6. On the Variation of the f-Inequality of a Random Variable

      • I. Cascos-Fernández, M. López-Díaz, M. A. Gil-Álvarez
      Pages 98-104

    7. Probability of Intuitionistic Fuzzy Events

      • Przemysław Grzegorzewski, Edyta Mrówka
      Pages 105-115

    8. A New Calculus for Linguistic Prototypes in Data Analysis

      • Jonathan Lawry
      Pages 116-125

    9. Upper Probabilities and Selectors of Random Sets

      • Enrique Miranda, Inés Couso, Pedro Gil
      Pages 126-133

    10. On Multivalued Logic and Probability Theory

      • Beloslav Riečan
      Pages 134-139

    11. Reversing the Order of Integration in Iterated Expectations of Compact Convex Random Sets

      • Luis J. Rodríguez-Muñiz, Miguel López-Díaz, María Ángeles Gil
      Pages 140-145

    12. Lower Previsions for Unbounded Random Variables

      • Matthias C. M. Troffaes, Gert de Cooman
      Pages 146-155

    13. A Hierarchical Uncertainty Model under Essentially Incomplete Information

      • Lev V. Utkin
      Pages 156-163

    14. Imprecise Calculation with the Qualitative Information about Probability Distributions

      • Lev V. Utkin
      Pages 164-169

    15. Approximation of Belief Functions by Minimizing Euclidean Distances

      • Thomas Weiler, Ulrich Bodenhofer
      Pages 170-177

    16. Variants of Defining the Cardinalities of Fuzzy Sets

      • Maciej Wygralak
      Pages 178-185
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Keywords

About this book

Classical probability theory and mathematical statistics appear sometimes too rigid for real life problems, especially while dealing with vague data or imprecise requirements. These problems have motivated many researchers to "soften" the classical theory. Some "softening" approaches utilize concepts and techniques developed in theories such as fuzzy sets theory, rough sets, possibility theory, theory of belief functions and imprecise probabilities, etc. Since interesting mathematical models and methods have been proposed in the frameworks of various theories, this text brings together experts representing different approaches used in soft probability, statistics and data analysis.

Editors and Affiliations

  • Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Przemysław Grzegorzewski, Olgierd Hryniewicz

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

    María Ángeles Gil

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