Ebook: Statistical Modeling, Analysis and Management of Fuzzy Data

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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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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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.
Content:
Front Matter....Pages I-XIV
Front Matter....Pages 1-1
Fuzziness and randomness....Pages 3-21
Front Matter....Pages 23-23
On the variance of random fuzzy variables....Pages 25-42
f-inequality indices for fuzzy random variables....Pages 43-63
Traditional techniques to prove some limit theorems for fuzzy random variables....Pages 64-71
Convergence in graph for fuzzy valued martingales and smartingales....Pages 72-89
Remarks on Korovkin-type approximation of fuzzy random variables....Pages 90-103
Several notions of differentiability for fuzzy set-valued mappings....Pages 104-116
Front Matter....Pages 117-117
Average level of a fuzzy set....Pages 119-126
Second order possibility measure induced by a fuzzy random variable....Pages 127-144
Measure extension from meet-systems and falling measures representation....Pages 145-159
The structure of fuzzy measure families induced by upper and lower probabilities....Pages 160-172
Statistical classes and fuzzy set theoretical classification of probability distributions....Pages 173-195
Front Matter....Pages 197-197
Statistics with one-dimensional fuzzy data....Pages 199-212
Testing fuzzy hypotheses with vague data....Pages 213-225
Possibilistic interpretation of fuzzy statistical tests....Pages 226-238
Possibilistic regression analysis....Pages 239-254
Linear regression in a fuzzy context. The least square method....Pages 255-281
Linear regression with random fuzzy observations....Pages 282-305
Back Matter....Pages 307-309

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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.
Content:
Front Matter....Pages I-XIV
Front Matter....Pages 1-1
Fuzziness and randomness....Pages 3-21
Front Matter....Pages 23-23
On the variance of random fuzzy variables....Pages 25-42
f-inequality indices for fuzzy random variables....Pages 43-63
Traditional techniques to prove some limit theorems for fuzzy random variables....Pages 64-71
Convergence in graph for fuzzy valued martingales and smartingales....Pages 72-89
Remarks on Korovkin-type approximation of fuzzy random variables....Pages 90-103
Several notions of differentiability for fuzzy set-valued mappings....Pages 104-116
Front Matter....Pages 117-117
Average level of a fuzzy set....Pages 119-126
Second order possibility measure induced by a fuzzy random variable....Pages 127-144
Measure extension from meet-systems and falling measures representation....Pages 145-159
The structure of fuzzy measure families induced by upper and lower probabilities....Pages 160-172
Statistical classes and fuzzy set theoretical classification of probability distributions....Pages 173-195
Front Matter....Pages 197-197
Statistics with one-dimensional fuzzy data....Pages 199-212
Testing fuzzy hypotheses with vague data....Pages 213-225
Possibilistic interpretation of fuzzy statistical tests....Pages 226-238
Possibilistic regression analysis....Pages 239-254
Linear regression in a fuzzy context. The least square method....Pages 255-281
Linear regression with random fuzzy observations....Pages 282-305
Back Matter....Pages 307-309
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