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V. Krätschmer (2001)
A unified approach to fuzzy random variables
Fuzzy Sets and Systems 123:1–9.
The concept of fuzzy random variable was introduced as an analogous notion to random variables in order to extend
statistical analysis to situations when the outcomes of some random experiment are fuzzy sets. But in contrary to the classical statistical methods no unique de nition has been established yet. In this paper a set-theoretical concept of fuzzy random variable will be presented. This notion provides a useful framework to compare different concepts of fuzzy random variables, using methods of general topology and drawing on results from topological measure theory and the theory of analytic spaces. As the main result, it will be shown that the introduced concept of fuzzy random variable is a uni cation of the already known ones.
