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Statistical Modeling, Analysis and Management of Fuzzy Data : Studies in Fuzziness and Soft Computing - Carlo Bertoluzza

Statistical Modeling, Analysis and Management of Fuzzy Data

Studies in Fuzziness and Soft Computing

By: Carlo Bertoluzza (Editor), Maria A. Gil (Editor), Dan A. Ralescu (Editor)

Hardcover Published: 11th January 2002
ISBN: 9783790814408
Number Of Pages: 309

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"Statistical Modeling, Analysis and Management of Fuzzy Data," or SMFD for short, is an important contribution to a better understanding of a basic issue -an issue which has been controversial, and still is though to a lesser degree. In substance, the issue is: are fuzziness and randomness distinct or coextensive facets of uncertainty? Are the theories of fuzziness and random- ness competitive or complementary? In SMFD, these and related issues are addressed with rigor, authority and insight by prominent contributors drawn, in the main, from probability theory, fuzzy set theory and data analysis com- munities. First, a historical perspective. The almost simultaneous births -close to half a century ago-of statistically-based information theory and cybernetics were two major events which marked the beginning of the steep ascent of probability theory and statistics in visibility, influence and importance. I was a student when information theory and cybernetics were born, and what is etched in my memory are the fascinating lectures by Shannon and Wiener in which they sketched their visions of the coming era of machine intelligence and automation of reasoning and decision processes. What I heard in those lectures inspired one of my first papers (1950) "An Extension of Wiener's Theory of Prediction," and led to my life-long interest in probability theory and its applications to information processing, decision analysis and control.

Foreword
Preface
Contents
Fuzziness and Randomness
Fuzziness and randomnessp. 3
Fuzzy-Valued Random Elements
On the variance of random fuzzy variablesp. 25
f-inequality indices for fuzzy random variablesp. 43
Traditional techniques to prove some limit theorems for fuzzy random variablesp. 64
Convergence in graph for fuzzy valued martingales and smartingalesp. 72
Remarks on Korovkin-type approximation of fuzzy random variablesp. 90
Several notions of differentiability for fuzzy set-valued mappingsp. 104
Possibility, Probability and Fuzzy Measures
Average level of a fuzzy setp. 119
Second order possibility measure induced by a fuzzy random variablep. 127
Measure extension from meet-systems and falling measures representationp. 145
The structure of fuzzy measure families induced by upper and lower probabilitiesp. 160
Statistical classes and fuzzy set theoretical classification of probability distributionsp. 173
Statistics and Fuzzy Data Analysis
Statistics with one-dimensional fuzzy datap. 199
Testing fuzzy hypotheses with vague datap. 213
Possibilistic interpretation of fuzzy statistical testsp. 226
Possibilistic regression analysisp. 239
Linear regression in a fuzzy context. The least square methodp. 255
Linear regression with random fuzzy observationsp. 282
Indexp. 307
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783790814408
ISBN-10: 3790814407
Series: Studies in Fuzziness and Soft Computing
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 309
Published: 11th January 2002
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.91
Weight (kg): 0.64