Soft Methods for Integrated Uncertainty Modelling

1. Front Matter

   Pages I-X

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2. Keynote Papers

   1. Front Matter

      Pages I-X

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   2. Generalized Theory of Uncertainty (GTU) – Principal Concepts and Ideas

      • Lotfi A. Zadeh

      Pages 3-4

   3. Reasoning with Vague Probability Assessments

      • Gert de Cooman

      Pages 5-6

   4. Soft Methods in Earth Systems Engineering

      • Jim W. Hall

      Pages 7-10

   5. Statistical Data Processing under Interval Uncertainty: Algorithms and Computational Complexity

      • Vladik Kreinovich

      Pages 11-26

3. Soft Methods in Statistics and Random Information Systems

   1. Front Matter

      Pages I-X

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   2. On Testing Fuzzy Independence

      • Olgierd Hryniewicz

      Pages 29-36

   3. Variance Decomposition of Fuzzy Random Variables

      • Andreas Wünsche, Wolfgang Näther

      Pages 37-44

   4. Fuzzy Histograms and Density Estimation

      • Kevin Loquin, Olivier Strauss

      Pages 45-52

   5. Graded Stochastic Dominance as a Tool for Ranking the Elements of a Poset

      • Karel De Loof, Hans De Meyer, Bernard De Baets

      Pages 53-60

   6. On Neyman-Pearson Lemma for Crisp, Random and Fuzzy Hypotheses

      • Adel Mohammadpour, Ali Mohammad-Djafari

      Pages 61-69

   7. Fuzzy Probability Distributions Induced by Fuzzy Random Vectors

      • Wolfgang Trutschnig

      Pages 71-78

   8. On the Identifiability of TSK Additive Fuzzy Rule-Based Models

      • José Luis Aznarte M., José Manuel Benítez

      Pages 79-86

   9. An Asymptotic Test for Symmetry of Random Variables Based on Fuzzy Tools

      • González-Rodríguez G., Colubi A., D’Urso P., Giordani P.

      Pages 87-94

   10. Exploratory Analysis of Random Variables Based on Fuzzifications

       • Colubi A., González-Rodríguez G., Lubiano M.A., Montenegro M.

       Pages 95-102

   11. A Method to Simulate Fuzzy Random Variables

       • González-Rodríguez G., Colubi A., Gil M.A., Coppi R.

       Pages 103-110

   12. Friedman’s Test for Ambiguous and Missing Data

       • Edyta Mrówka, Przemysław Grzegorzewski

       Pages 111-118

4. Probability of Imprecisely-Valued Random Elements with Applications

   1. Front Matter

      Pages I-X

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   2. Measure-Free Martingales with Application to Classical Martingales

      • S.F. Cullender, W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson

      Pages 121-128

The idea of soft computing emerged in the early 1990s from the fuzzy systems c- munity, and refers to an understanding that the uncertainty, imprecision and ig- rance present in a problem should be explicitly represented and possibly even - ploited rather than either eliminated or ignored in computations. For instance, Zadeh de?ned ‘Soft Computing’ as follows: Soft computing differs from conventional (hard) computing in that, unlike hard computing, it is tolerant of imprecision, uncertainty and partial truth. In effect, the role model for soft computing is the human mind. Recently soft computing has, to some extent, become synonymous with a hybrid approach combining AI techniques including fuzzy systems, neural networks, and biologically inspired methods such as genetic algorithms. Here, however, we adopt a more straightforward de?nition consistent with the original concept. Hence, soft methods are understood as those uncertainty formalisms not part of mainstream s- tistics and probability theory which have typically been developed within the AI and decisionanalysiscommunity.Thesearemathematicallysounduncertaintymodelling methodologies which are complementary to conventional statistics and probability theory.

• artificial intelligence
• complex system
• complex systems
• computer-aided design (CAD)
• intelligence
• knowledge
• modeling
• modelling
• operations research
• statistics
• uncertainty

• AI Group Department of Engineering Mathematics, University of Bristol, Bristol, UK

  Jonathan Lawry

• Statistics and Operations Research, Rey Juan Carlos University, Spain

  Enrique Miranda

• Intelligent Systems Group Department of Electronics & Computer Science, University of Santiago de Compostela Santiago de Compostela, Spain

  Alberto Bugarin

• Department of Applied Mathematics, Beijing University of Technology, Beijing, P.R. China

  Shoumei Li

• Dpto. Estadistica e I.O y D.M. Calle Calvo Sotelo s/n, Universiad de Oviedo Fac. Ciencias, Oviedo, Spain

  Maria Angeles Gil

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

  Przemys aw Grzegorzewski, Olgierd Hyrniewicz

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