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Fuzzy random variable is a measurable mapping from a probability space to a collection of fuzzy variables.
The so-called birandom variable is a measurable mapping from a probability space to a collection of random variables.
Fuzzy random variable is a mapping from a probability space to a collection of fuzzy variables, it is an appropriate tool to deal with twofold uncertainty with fuzziness and randomness in an optimization framework.
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Consider a probability space (Ω, A, Pr) with domain Ω and probability Pr that an element of Ω is within the set A. Assuming that ξ is a function from the probability space (Ω, A, Pr) to the fuzzy set, if for any Borel set B on real number field R, and any ω in Ω, Pos{ξ ∊ B} is a measurable function of ω, then ξ is a fuzzy stochastic variable.
Then, is a probability space.
Let be a probability space.
Call P a probability function, and (Ω, F, P) a probability space.
( O, F, P ) : a probability space.
Let (P, Ω, A) be a probability space.
In probabilistic approaches to causation, causal relata are represented by events in a probability space.
If and is -integrable, where is a probability space, then.
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