Statistical Modeling, Analysis and Management of Fuzzy Data模糊数据的统计建模、分析与管理
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作者： Carlo Bertoluzza等著
出 版 社：
出版时间： 2002-9-1字数：版次： 1页数： 309印刷时间： 2002/09/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783790814408包装： 精装内容简介
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.
目录
Foreword
Preface
Contents
PART 1. FUZZINESS AND RANDOMNESS
Fuzziness and randomness
PART 2. FUZZY-VALUED RANDOM ELEMENTS
On the variance of random fuzzy variables
f-inequality indices for fuzzy random variables
Traditional techniques to prove some limit theorems for fuzzy random variables
Convergence in graph for fuzzy valued martingales and smartingales
Remarks on Korovkin-type approximation of fuzzy random variables
Several notions of differentiability for fuzzy set-valued mappings
PART 3. POSSIBILITY, PROBABILITY AND FUZZY MEASURES
Average level of a fuzzy set
Second order possibility measure induced by a fuzzy random variable
Measure extension from meet-systems and falling measures representation
The structure of fuzzy measure families induced by upper and lower probabilities
Statistical classes and fuzzy set theoretical classification of probability distributions
PART 4. STATISTICS AND FUZZY DATA ANALYSIS
Statistics with one-dimensional fuzzy data
Testing fuzzy hypotheses with vague data
Possibilistic interpretation of fuzzy statistical tests
Possibilistic regression analysis
Linear regression in a fuzzy context. The least square method
Linear regression with random fuzzy observations
INDEX
