Abstract
Abstract A generated fuzzy σ-algebra equipped by Giles fuzzy connectives is considered as a basis of this paper. Starting from a simple fuzzy measurable function, we introduce the notion of a fuzzy measurable function. A one-to-one correspondence between the fuzzy measurable functions and the random variables with values in the fuzzy real line is shown. An inverse of a fuzzy measurable function is proved to be an extended T ∞ -fuzzy observable and vice versa. Linear operations on fuzzy measurable functions are introduced.
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