Geidelberg: Physica-Verlag, 2002. — 376 p.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.Contents :Front MatterFront Matter Quantitative Possibility Theory and its Probabilistic Connections Toward a Perception-Based Theory of Probabilistic Reasoning with Imprecise ProbabilitiesFront Matter Independence and Conditioning in a Connectivistic Fuzzy Logic Framework About Ideals on the Set of Fuzzy Measures Operators for Convolution of Fuzzy Measures Probabilities of Fuzzy Events Based on Scalar Cardinalities On the Variation of the f -Inequality of a Random Variable Probability of Intuitionistic Fuzzy Events A New Calculus for Linguistic Prototypes in Data Analysis Upper Probabilities and Selectors of Random Sets On Multivalued Logic and Probability Theory Reversing the Order of Integration in Iterated Expectations of Compact Convex Random Sets Lower Previsions for Unbounded Random Variables A Hierarchical Uncertainty Model under Essentially Incomplete Information Imprecise Calculation with the Qualitative Information about Probability Distributions Approximation of Belief Functions by Minimizing Euclidean Distances Variants of Defining the Cardinalities of Fuzzy SetsFront Matter Probabilistic Reasoning in Fuzzy Rule-Based Systems Acceptance Sampling Plans by Variables for Vague Data Possibilistic Approach to the Bayes Statistical DecisionsFront Matter Fuzzy Comparison of Frequency Distributions Test of One-Sided Hypotheses on the Expected Value of a Fuzzy Random Variable Blackwell Sufficiency and Fuzzy Experiments Optimal Stopping in Fuzzy Stochastic Processes and its Application to Option Pricing in Financial EngineeringFront Matter Fuzzy Conjoint Analysis Grade Analysis of Repeated Multivariate Measurements A Contribution to Stochastic Modeling Volcanic Petroleum Reservoir Improving the Quality of Association Rule Mining by Means of Rough Sets Towards Fuzzy c-means Based Microaggregation Statistical Profiles of Words for Ontology Enrichment Quest on New Applications for Dempster-Shafer Theory: Risk Analysis in Project Profitability Calculus Decision Making Based on Informational Variables An Algorithm for Identifying Fuzzy Measures with Ordinal Information Exploring an Alternative Method for Handling Inconsistency in the Fusion of Expert and Learnt Information Approximate Reasoning Schemes: Classifiers for Computing with Words Using Consensus Methods to User Classification in Interactive Systems Aggregation Methods to Evaluate Multiple Protected Versions of the Same Confidential Data Set On Multivariate Fuzzy Time Series Analysis and Forecasting
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