6Fuzzy Statistics
The uncertainty characterizing decisions and indeed the process of decision‐making on the basis of statistical reasoning can be traced, in many cases, to the lack of imprecise information coming from vagueness in the data considered. In this sense, fuzzy set theory comes to the forefront and, as it is plausibly expected, it plays a prominent role. Before inserting fuzziness, we will present a brief review of random variables (also known as stochastic variables) and their properties as well as the classical statistical notions of point estimation, interval estimation, hypothesis testing, and regression. Then, their fuzzy analogues will be introduced.
6.1 Random Variables
A mapping from the set 
of possible outcomes (sample points) of an experiment to a subset of real numbers 
is a random variable. A rigorous definition of a random variable is the following:
Some remarks are in order at this point:
- a random ...
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