Soft Methods in Probability, Statistics and Data Analysis

✍ Scribed by Didier Dubois, Henri Prade (auth.), Dr. Przemysław Grzegorzewski, Prof. Dr. Olgierd Hryniewicz, Professor María Ángeles Gil (eds.)

Publisher: Physica-Verlag Heidelberg
Year: 2002
Tongue: English
Leaves: 376
Series: Advances in Intelligent and Soft Computing 16
Edition: 1
Category: Library

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✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-X
Front Matter....Pages 1-1
Quantitative Possibility Theory and its Probabilistic Connections....Pages 3-26
Toward a Perception-Based Theory of Probabilistic Reasoning with Imprecise Probabilities....Pages 27-61
Front Matter....Pages 63-63
Independence and Conditioning in a Connectivistic Fuzzy Logic Framework....Pages 65-75
About Ideals on the Set of Fuzzy Measures....Pages 76-83
Operators for Convolution of Fuzzy Measures....Pages 84-91
Probabilities of Fuzzy Events Based on Scalar Cardinalities....Pages 92-97
On the Variation of the f -Inequality of a Random Variable....Pages 98-104
Probability of Intuitionistic Fuzzy Events....Pages 105-115
A New Calculus for Linguistic Prototypes in Data Analysis....Pages 116-125
Upper Probabilities and Selectors of Random Sets....Pages 126-133
On Multivalued Logic and Probability Theory....Pages 134-139
Reversing the Order of Integration in Iterated Expectations of Compact Convex Random Sets....Pages 140-145
Lower Previsions for Unbounded Random Variables....Pages 146-155
A Hierarchical Uncertainty Model under Essentially Incomplete Information....Pages 156-163
Imprecise Calculation with the Qualitative Information about Probability Distributions....Pages 164-169
Approximation of Belief Functions by Minimizing Euclidean Distances....Pages 170-177
Variants of Defining the Cardinalities of Fuzzy Sets....Pages 178-185
Front Matter....Pages 187-187
Probabilistic Reasoning in Fuzzy Rule-Based Systems....Pages 189-196
Acceptance Sampling Plans by Variables for Vague Data....Pages 197-206
Possibilistic Approach to the Bayes Statistical Decisions....Pages 207-218
Front Matter....Pages 187-187
Fuzzy Comparison of Frequency Distributions....Pages 219-227
Test of One-Sided Hypotheses on the Expected Value of a Fuzzy Random Variable....Pages 228-235
Blackwell Sufficiency and Fuzzy Experiments....Pages 236-243
Optimal Stopping in Fuzzy Stochastic Processes and its Application to Option Pricing in Financial Engineering....Pages 244-251
Front Matter....Pages 253-253
Fuzzy Conjoint Analysis....Pages 255-265
Grade Analysis of Repeated Multivariate Measurements....Pages 266-273
A Contribution to Stochastic Modeling Volcanic Petroleum Reservoir....Pages 274-280
Improving the Quality of Association Rule Mining by Means of Rough Sets....Pages 281-288
Towards Fuzzy c-means Based Microaggregation....Pages 289-294
Statistical Profiles of Words for Ontology Enrichment....Pages 295-301
Quest on New Applications for Dempster-Shafer Theory: Risk Analysis in Project Profitability Calculus....Pages 302-309
Decision Making Based on Informational Variables....Pages 310-320
An Algorithm for Identifying Fuzzy Measures with Ordinal Information....Pages 321-328
Exploring an Alternative Method for Handling Inconsistency in the Fusion of Expert and Learnt Information....Pages 329-337
Approximate Reasoning Schemes: Classifiers for Computing with Words....Pages 338-345
Using Consensus Methods to User Classification in Interactive Systems....Pages 346-354
Aggregation Methods to Evaluate Multiple Protected Versions of the Same Confidential Data Set....Pages 355-362
On Multivariate Fuzzy Time Series Analysis and Forecasting....Pages 363-372

✦ Subjects

Probability and Statistics in Computer Science; Statistics for Business/Economics/Mathematical Finance/Insurance; Artificial Intelligence (incl. Robotics); Probability Theory and Stochastic Processes

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