Statistical Modeling, Analysis and Management of Fuzzy Data

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Bertoluzza, Carlo (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Gil, Maria A. (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Ralescu, Dan A. (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Heidelberg : Physica-Verlag HD : Imprint: Physica, 2002.
• Έκδοση: 1st ed. 2002.
• Σειρά: Studies in Fuzziness and Soft Computing, 87
• Θέματα: Statistics .; Artificial intelligence.; Probabilities.; Statistics and Computing/Statistics Programs.; Artificial Intelligence.; Probability Theory and Stochastic Processes.

 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. 

 1. Fuzziness and Randomness -- Fuzziness and randomness -- 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 -- 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 -- 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.