Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy- and real-valued data

The expected value of a fuzzy random variable plays an important role as central summary measure, and for this reason, in the last years valuable statistical inferences about the means of the fuzzy random variables have been developed. Some of the main contributions in this topic are gathered and discussed. Concerning the hypothesis testing, the bootstrap techniques have empirically shown to be efficient and powerful. Algorithms to apply these techniques in practice and some illustrative real-life examples are included. On the other hand, it has been recently shown that the distribution of any real-valued random variable can be represented by means of a fuzzy set. The characterizing fuzzy sets correspond to the expected value of a certain fuzzy random variable based on a family of fuzzy-valued transformations of the original real-valued ones. They can be used for descriptive/exploratory or inferential purposes. This fact adds an extra-value to the fuzzy expected value and the preceding statistical procedures, that can be used in statistics about real distributions.