A fuzzy conditional expectation with respect to sub σ-algebra of for a fuzzy random variable is introduced in the complete probability space (Ω, p), and the fact that such a fuzzy conditional expectation exists uniquely is proved and its some properities are discussed.
The settlenment rate lof piletop is used to describe the bearing process of piles and the settlenment rate lis taken as a fuzzy random variable considering the fuzziness and randomness of the failure of piles.
Finally, we design some algorithms about fuzzy random simulations to compute the mean chance of fuzzy random event, find the optimistic value of a return function, and evaluate the expected value of a fuzzy random variable.
The concept of fuzzy random variable, mean and variance of fuzzy random variable, minimum of fuzzy numbers are used in the model.
One of the concepts defined by Liu and Liu (2003a) is that the fuzzy random variable is a measurable function from a probability space to a collection of fuzzy variables and its expected value is described as a scalar number.
The concept of fuzzy random variable (FRV), mean and variance of FRV is used in the model.
Some properties concerning the measurability of fuzzy random variable are also discussed.
This paper presents a new definition of fuzzy random variable, and gives a novel definition of scalar expected value operator for fuzzy random variables.