Dealing with randomness and vagueness in business and management sciences: the fuzzy-probabilistic approach as a tool for the study of statistical relationships between imprecise variables

In practical applications relating to business and management sciences, there are many variables that, for their own nature, are better described by a pair of ordered values (i.e. financial data). By summarizing this measurement with a single value, there is a loss of information; thus, in these situations, data are better described by interval values rather than by single values. Interval arithmetic studies and analyzes this type of imprecision; however, if the intervals has no sharp boundaries, fuzzy set theory is the most suitable instrument. Moreover, fuzzy regression models are able to overcome some typical limitation of classical regression because they do not need the same strong assumptions. In this paper, we present a review of the main methods introduced in the literature on this topic and introduce some recent developments regarding the concept of randomness in fuzzy regression