Soft Methods for Handling Variability and Imprecision

  • Didier Dubois
  • M. Asunción Lubiano
  • Henri Prade
  • María Ángeles Gil
  • Przemysław Grzegorzewski
  • Olgierd Hryniewicz

Part of the Advances in Soft Computing book series (AINSC, volume 48)

Table of contents

  1. Front Matter
  2. Invited Papers

  3. Foundations

    1. Front Matter
      Pages 33-33
    2. Jonathan Lawry, Yongchuan Tang
      Pages 35-42
    3. Marco E. G. V. Cattaneo
      Pages 43-50
    4. Giulianella Coletti, Romano Scozzafava, Barbara Vantaggi
      Pages 51-58
    5. Andrew Schumann
      Pages 59-65
    6. Sébastien Destercke, Gert de Cooman
      Pages 66-73
  4. Statistical Methods

    1. Front Matter
      Pages 81-81
    2. Statistical Inference

    3. Statistical Tests

      1. Ángela Blanco, Ana Colubi, Norberto Corral, Gil González-Rodríguez
        Pages 111-117
      2. Inés Couso, Luciano Sánchez
        Pages 126-132
      3. Manuel Montenegro, María Rosa Casals, Ana Colubi, María Ángeles Gil
        Pages 133-139
      4. Ana Belén Ramos, Gil González-Rodríguez, Ana Colubi, María Ángeles Gil
        Pages 140-146
      5. M. Asunción Lubiano, Ana Colubi, Gil González-Rodríguez
        Pages 147-154
      6. Olgierd Hryniewicz, Anna Szediw
        Pages 155-162
    4. Estimation

      1. Etienne Côme, Latifa Oukhellou, Thierry Denœux, Patrice Aknin
        Pages 165-174
      2. Kevin Loquin, Olivier Strauss
        Pages 175-182
      3. Jonathan Lawry, Inés González-Rodríguez
        Pages 183-189
      4. Ana Colubi, María Ángeles Gil, Gil González-Rodríguez, María Teresa López
        Pages 190-197
  5. Mathematical Aspects

    1. Front Matter
      Pages 199-199
    2. Invited Session: Fuzzy Set-Valued Analysis

      1. Luciano Stefanini
        Pages 203-210
      2. Luis J. Rodríguez-Muñiz
        Pages 211-217
      3. Rosana Rodríguez-López
        Pages 218-225
      4. Andrés D. Báez-Sánchez, Marko A. Rojas-Medar
        Pages 226-231
    3. Measure Theory

      1. Enrique Miranda, Matthias C. M. Troffaes, Sébastien Destercke
        Pages 235-242
      2. Gert de Cooman, Enrique Miranda
        Pages 243-252
    4. Differential Equations

    5. Convergence Results

    6. Combinatorics of Imprecise Probabilities

    7. Variance in Generalized Probability Representations

      1. Erik Quaeghebeur
        Pages 323-330
      2. Ángela Blanco, Norberto Corral, Gil González-Rodríguez, M. Asunción Lubiano
        Pages 331-337
    8. Aggregation Functions

      1. Isabel Aguiló, Javier Martín, Gaspar Mayor, Jaume Suñer
        Pages 341-348
      2. Fabrizio Durante, Susanne Saminger-Platz, Peter Sarkoci
        Pages 349-356
  6. Engineering

    1. Front Matter
      Pages 357-357
    2. Computational Methods

About these proceedings


Probability theory has been the only well-founded theory of uncertainty for a long time. It was viewed either as a powerful tool for modelling random phenomena, or as a rational approach to the notion of degree of belief. During the last thirty years, in areas centered around decision theory, artificial intelligence and information processing, numerous approaches extending or orthogonal to the existing theory of probability and mathematical statistics have come to the front. The common feature of those attempts is to allow for softer or wider frameworks for taking into account the incompleteness or imprecision of information. Many of these approaches come down to blending interval or fuzzy interval analysis with probabilistic methods.

This book gathers contributions to the 4th International Conference on Soft methods in Probability and Statistics. Its aim is to present recent results illustrating such new trends that enlarge the statistical and uncertainty modeling traditions, towards the handling of incomplete or subjective information. It covers a broad scope ranging from philosophical and mathematical underpinnings of new uncertainty theories, with a stress on their impact in the area of statistics and data analysis, to numerical methods and applications to environmental risk analysis and mechanical engineering. A unique feature of this collection is to establish a dialogue between fuzzy random variables and imprecise probability theories.


Bayesian inference Binomial distribution Cyc Imprecise probability Measure Probability theory Random variable Revision artificial intelligence decision theory information processing modeling optimization semantics uncertainty

Editors and affiliations

  • Didier Dubois
    • 1
  • M. Asunción Lubiano
    • 2
  • Henri Prade
    • 1
  • María Ángeles Gil
    • 2
  • Przemysław Grzegorzewski
    • 3
  • Olgierd Hryniewicz
    • 4
  1. 1.Université Paul SabatierToulouseFrance
  2. 2.Universidad de OviedoSpain
  3. 3.Polish Academy of SciencesWarsawPoland
  4. 4.Polish Academy of Sciences,WarsawPoland

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-540-85026-7
  • Online ISBN 978-3-540-85027-4
  • Series Print ISSN 1615-3871
  • Series Online ISSN 1860-0794
  • Buy this book on publisher's site