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The contributions in this book state the complementary rather than competitive relationship between Probability and Fuzzy Set Theory and allow solutions to real life problems with suitable combinations of both theories.
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.