Soft Methods in Probability, Statistics and Data Analysis

1. Front Matter

   Pages I-X

   PDF

2. Introductory Papers

   1. Front Matter

      Pages 1-1

      PDF

   2. Quantitative Possibility Theory and its Probabilistic Connections

      • Didier Dubois, Henri Prade

      Pages 3-26

   3. Toward a Perception-Based Theory of Probabilistic Reasoning with Imprecise Probabilities

      • Lotfi A. Zadeh

      Pages 27-61

3. Soft Methods in Probability: Fundamentals

   1. Front Matter

      Pages 63-63

      PDF

   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

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.

• Analysis
• Probability theory
• Stochastic model
• Stochastic models
• data analysis
• fuzzy
• mathematical statistics
• sets
• statistics

• 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

Policies and ethics