By L. Rosenfeld

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123, 39–48 (2001) 82. : Fuzzy information and decisions in statistical model. , et al. ) Advances in Fuzzy Sets Theory and Applications, pp. 303–320. North-Holland, Amsterdam (1979) 83. : Extensional versus intuitive reasoning: the conjunctive fallacy in probability judgements. Psychol. Rev. 91, 293–315 (1983) 84. : Is it necessary to develop a fuzzy Bayesian inference. In: Viertl, R. ) Probability and Bayesian Statistics, pp. 471–475. Plenum, New York (1987) 85. : Statistical methods for non-precise data.

X1 ; : : : ; Xn I 1 ı/; 1/. e. x1 ; : : : ; xn I 1 ı/ holds. x1 ; : : : ; xn I 1 ı/ is the observed value of U 1 n the upper limit of the one-sided confidence interval . X1 ; : : : ; Xn I 1 ı/ on a confidence level 1 ı. x1 ; : : : ; xn I 1 ı=2/. Thus, 2 On Joint Modelling of Random Uncertainty and Fuzzy Imprecision 27 when we test a hypothesis about the value of the parameter # we find a respective confidence interval, and compare it to the hypothetical value. Dubois et al. [22] proposed to use statistical confidence intervals of parameters of probability distributions for the construction of possibility distributions of these parameters in a fully objective way.

R/ be the space of all fuzzy numbers. e W Given a probability space . ; A; P /, a mapping X ! 0; 1 the set-valued mappings X˛ W ! //˛ , are random sets subsets of R , defined so that for all ! Rp /). Fuzzy random variables may be used to model random and imprecise measurements. First statistical methods for the analysis of such imprecise fuzzy data were developed in the 1980s. Kruse and Meyer [53] proposed a general methodology for dealing with fuzzy random data. 2. This assumption has very important practical consequences.