Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics

Abstract

Fuzzy sets generalize the concept of sets by considering that elements belong to a class (or fulfil a property) with a degree of membership (or certainty) ranging between 0 and 1. Fuzzy sets have been used in diverse areas to model gradual transitions as opposite to abrupt changes. In econometrics and statistics, this has been especially relevant in clustering, regression discontinuity designs, and imprecise data modelling, to name but a few. Although the membership functions vary between 0 and 1 as the probabilities, the nature of the imprecision captured by the fuzzy sets is usually different from stochastic uncertainty. The aim is to illustrate the advantages of combining fuzziness, imprecision, or partial knowledge with randomness through various key methodological problems. Emphasis will be placed on the management of non-precise data modelled through (fuzzy) sets. Software to apply the reviewed methodology will be suggested. Some open problems that could be of future interest will be discussed.