Statistical Modeling, Analysis and Management of Fuzzy Data Book

	Foreword
	Preface
	Contents
Pt. 1	Fuzziness and Randomness
	Fuzziness and randomness	3
Pt. 2	Fuzzy-Valued Random Elements
	On the variance of random fuzzy variables	25
	f-inequality indices for fuzzy random variables	43
	Traditional techniques to prove some limit theorems for fuzzy random variables	64
	Convergence in graph for fuzzy valued martingales and smartingales	72
	Remarks on Korovkin-type approximation of fuzzy random variables	90
	Several notions of differentiability for fuzzy set-valued mappings	104
Pt. 3	Possibility, Probability and Fuzzy Measures
	Average level of a fuzzy set	119
	Second order possibility measure induced by a fuzzy random variable	127
	Measure extension from meet-systems and falling measures representation	145
	The structure of fuzzy measure families induced by upper and lower probabilities	160
	Statistical classes and fuzzy set theoretical classification of probability distributions	173
Pt. 4	Statistics and Fuzzy Data Analysis
	Statistics with one-dimensional fuzzy data	199
	Testing fuzzy hypotheses with vague data	213
	Possibilistic interpretation of fuzzy statistical tests	226
	Possibilistic regression analysis	239
	Linear regression in a fuzzy context. The least square method	255
	Linear regression with random fuzzy observations	282
	Index	307