On the variance of fuzzy random variables
Fuzzy Sets and Systems
Information Sciences: an International Journal
Gaussian fuzzy random variables
Fuzzy Sets and Systems
Asymptotic properties of least squares estimation with fuzzy observations
Information Sciences: an International Journal
Management of uncertainty in Statistical Reasoning: The case of Regression Analysis
International Journal of Approximate Reasoning
Estimation of a simple linear regression model for fuzzy random variables
Fuzzy Sets and Systems
Regression with fuzzy random data
Computational Statistics & Data Analysis
Least squares estimation of a linear regression model with LR fuzzy response
Computational Statistics & Data Analysis
Reduction to least-squares estimates in multiple fuzzy regression analysis
IEEE Transactions on Fuzzy Systems
A decomposition theorem for fuzzy set-valued random variables
Fuzzy Sets and Systems
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Let X˜,Y˜ be two convex fuzzy random variables on Rn. Using a suitable metric we prove that the conditional expectation E(Y˜ | X˜) is the best approximation of Y˜ by measurable functions of X˜. This generalizes the analogous and well known property for real random variables. A further topic is the approximation of Y˜ by a linear function of X˜. In special cases and by use of Hukuhara's difference between fuzzy sets, we obtain formulas which are analogous to the classical structure. Contrary to the classical fact, however, the conditional expectation of Gaussian fuzzy random variables in general does not coincide with the linear regression function.