25.4 Further results
A fuzzy stochastic quantity x* in LR-form is defined by four real random variables m, s, l and r with and two fuzzy numbers
In order to fulfill the random variables m, s, l and r have to be square-integrable. By the linearity of the expectation operator the expectation X* is a fuzzy number in LR-form obeying
The variance of this fuzzy random quantity is given by
Many results for real random variables can be generalized for fuzzy random quantities.
Proposition 25.2 (Chebysheff’s inequality):
For fuzzy stochastic quantities X* with < ∞ the following holds:
By the ...