Statistical Modeling, Analysis and Management of Fuzzy Data (Studies in Fuzziness and Soft Computing)

Statistical Modeling, Analysis and Management of Fuzzy Data (Studies in Fuzziness and Soft Computing)

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Language English
Contributor(s) Carlo Bertoluzza, Maria A. Gil, Dan A. Ralescu
Binding Hardcover
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Overview: Statistical Modeling

The contributions in this book state the complementary rather than competitive relationship between Probability and Fuzzy Set Theory and allow solutions to real life problems with suitable combinations of both theories. Table Of Contents: ForewordPrefaceContentsPt. 1Fuzziness and RandomnessFuzziness and randomness3Pt. 2Fuzzy-Valued Random ElementsOn the variance of random fuzzy variables25f-inequality indices for fuzzy random variables43Traditional techniques to prove some limit theorems for fuzzy random variables64Convergence in graph for fuzzy valued martingales and smartingales72Remarks on Korovkin-type approximation of fuzzy random variables90Several notions of differentiability for fuzzy set-valued mappings104Pt. 3Possibility, Probability and Fuzzy MeasuresAverage level of a fuzzy set119Second order possibility measure induced by a fuzzy random variable127Measure extension from meet-systems and falling measures representation145The structure of fuzzy measure families induced by upper and lower probabilities160Statistical classes and fuzzy set theoretical classification of probability distributions173Pt. 4Statistics and Fuzzy Data AnalysisStatistics with one-dimensional fuzzy data199Testing fuzzy hypotheses with vague data213Possibilistic interpretation of fuzzy statistical tests226Possibilistic regression analysis239Linear regression in a fuzzy context. The least square method255Linear regression with random fuzzy observations282Index307

Features: Statistical Modeling

  • Mathematics
Product Details
Language English
Publication Date January 11, 2002
Publisher Physica
Contributor(s) Carlo Bertoluzza, Maria A. Gil, Dan A. Ralescu
Binding Hardcover
Edition 2002
Page Count 309
ISBN 10 3790814407
ISBN 13 9783790814408
Dimensions and Weight
Product Weight 635 grams
Product Dimensions 15.6 cm x 1.9 cm x 23.4 cm

Editorial Reviews

From the Back Cover

The contributions in this book connect Probability Theory/Statistics and Fuzzy Set Theory in different ways. Some of these connections are either philosophical or theoretical in nature, but most of them state models and methods to work with fuzzy data (or fuzzy perception) when dealing with random experiments. In this way, several probabilistic studies are developed, as well as techniques and criteria to get descriptive and inferential statistical conclusions from fuzzy data. On the other hand, some studies have been devoted to fuzzy measures and their relationship with measures in Probability Theory.
 

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