Statistical Modeling, Analysis and Management of Fuzzy Data

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

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Hardcover | 11 January 2002

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328 Pages

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23.5 x 15.88 x 2.54

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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.

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You Can Find This Book In

Non-Fiction Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory Mathematics Probability & Statistics Mathematical Foundation Set Theory Computing & I.T.Computer Science Artificial Intelligence

Medicine Medicine in General Applied Mathematics Fuzzy Set Theory Business Applications Mathematical & Statistical Software

Foreword
Preface
Contents
Fuzziness and Randomness
Fuzziness and randomness	p. 3
Fuzzy-Valued Random Elements
On the variance of random fuzzy variables	p. 25
f-inequality indices for fuzzy random variables	p. 43
Traditional techniques to prove some limit theorems for fuzzy random variables	p. 64
Convergence in graph for fuzzy valued martingales and smartingales	p. 72
Remarks on Korovkin-type approximation of fuzzy random variables	p. 90
Several notions of differentiability for fuzzy set-valued mappings	p. 104
Possibility, Probability and Fuzzy Measures
Average level of a fuzzy set	p. 119
Second order possibility measure induced by a fuzzy random variable	p. 127
Measure extension from meet-systems and falling measures representation	p. 145
The structure of fuzzy measure families induced by upper and lower probabilities	p. 160
Statistical classes and fuzzy set theoretical classification of probability distributions	p. 173
Statistics and Fuzzy Data Analysis
Statistics with one-dimensional fuzzy data	p. 199
Testing fuzzy hypotheses with vague data	p. 213
Possibilistic interpretation of fuzzy statistical tests	p. 226
Possibilistic regression analysis	p. 239
Linear regression in a fuzzy context. The least square method	p. 255
Linear regression with random fuzzy observations	p. 282
Index	p. 307
Table of Contents provided by Blackwell. All Rights Reserved.

Statistical Modeling, Analysis and Management of Fuzzy Data

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