Statistics with fuzzy random variables

摘要

The notion of Fuzzy Random Variable has been introduced to model random mechanisms generating imprecisely-valued data which can be properly described by means of fuzzy sets. Probabilistic aspects of these random elements have been deeply discussed in the literature. However, statistical analysis of fuzzy random variables has not received so much attention, in spite that implications of this analysis range over many fields, including Medicine, Sociology, Economics, and so on. A summary of the fundamentals of fuzzy random variables is presented. Then, some related "parameters" associated with the distribution of these variables are defined. Inferential procedures concerning these "parameters" are described. Some recent results related to linear models for fuzzy data are finally reviewed.