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

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 a...

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Bibliographic Details
Published in:Econometrics and statistics 2023-04, Vol.26, p.84-98
Main Authors: Colubi, Ana, Ramos-Guajardo, Ana Belén
Format: Article
Language:English
Subjects:
Fuzzy clustering
Fuzzy data
Fuzzy regression
Fuzzy regression discontinuity designs
Hilbert spaces
Interval data
Random (fuzzy) sets
Regression with fuzzy data
Set-valued data
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Summary: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.
ISSN:2452-3062
2452-3062
DOI:10.1016/j.ecosta.2022.07.001