On measurability and convergence in distribution of fuzzy random variables in the endograph metric

Miriam Alonso de la Fuente ()
Additional contact information
Miriam Alonso de la Fuente: Universidad de Oviedo, Departamento de Estadística e I. O. y D. M.

Fuzzy Optimization and Decision Making, 2025, vol. 24, issue 4, No 1, 614 pages

Abstract: Abstract Convergence in distribution of fuzzy random variables can be studied via the notion of weak convergence of random elements in general metric spaces, with the $$d_p$$ metrics being the most common. Our main objective is to prove new properties of this type of convergence with respect to the endograph metric and as a consequence show that this definition of convergence is suitable while working with this particular metric. We study some topological properties of the space of fuzzy sets with this metric and use them to prove a new version of the Skorokhod representation theorem for fuzzy random variables. Next, we study some continuous operations, such as the sum and product by a scalar, and state some results regarding convergence in distribution of fuzzy random variables with respect to the endograph metric. In conclusion, convergence in distribution of fuzzy random variables in the endograph metric is preserved by the usual operations, making this approach to convergence in distribution feasible.

Keywords: Convergence in distribution; Fuzzy random variable; Random set; Fuzzy set; Endograph metric (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10700-025-09456-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:fuzodm:v:24:y:2025:i:4:d:10.1007_s10700-025-09456-y

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10700

DOI: 10.1007/s10700-025-09456-y

Access Statistics for this article

Fuzzy Optimization and Decision Making is currently edited by Shu-Cherng Fang and Boading Liu

More articles in Fuzzy Optimization and Decision Making from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().