Fuzzy Random Expected Value of Variables

It should be pointed out that in order to avoid the case of oo — oo, at least one of the two integrals on the right side of formula (6.1) needs to be limited. Furthermore, the expression E on both sides of formula (6.1) have different meanings. The E on the left side stands for the expression of the fuzzy random variable while the E on the right side stands for the expression of the fuzzy variable, which is already reloaded. The reloading enables the expression E to have different definitions, which are indicated by the variables. 

Definition 6.2 Set to be a fuzzy random variable on probability space ( 2, A, Pr), 

Proof To prove E[i (o) is a random variable, we just need to proof [ (ft))] is a measurable function of m. We have 

Liu and Liu [3] also gave the proof that with two fuzzy random variables, if the expectation E[ ] E[rj, then t], with and / being fuzzy random variables. 

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