Ordered fuzzy random variables: Definition and the concept of normality
Authors:
- Adam Marszałek,
- Tadeusz Burczyński
Abstract
The concept of fuzzy random variable combines two sources of uncertainty: randomness and fuzziness, whereas the model of ordered fuzzy numbers provides a representation of inaccurate quantitative data, and is an alternative to the standard fuzzy numbers model proposed by Zadeh. This paper develops the model of ordered fuzzy numbers by defining the concept of fuzzy random variables for these numbers, called further ordered fuzzy random variables. Thanks to the well-defined arithmetic of ordered fuzzy numbers (existence of neutral and opposite elements) and the introduced ordered fuzzy random variables; it becomes possible to construct fully fuzzy stochastic time series models such as e.g., the autoregressive model or the GARCH model in the form of classical equations, which can be estimated using the least-squares or the maximum likelihood method. Furthermore, the concept of normality of ordered fuzzy random variables and the method to generate pseudo-random ordered fuzzy variables with normal distribution are introduced.
- Record ID
- CUT5fe83f13c7a14b1e8b3f4b9e2098c2bd
- Publication categories
- ;
- Author
- Journal series
- Information Sciences, ISSN 0020-0255, e-ISSN 1872-6291
- Issue year
- 2021
- Vol
- 545
- Pages
- 415-426
- Other elements of collation
- tab.; wykr.; Bibliografia (na s.) - 425-426; Bibliografia (liczba pozycji) - 37; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 545
- Keywords in English
- ordered fuzzy numbers, fuzzy random variables, ordered fuzzy random variables, normal ordered fuzzy random variable
- DOI
- DOI:10.1016/j.ins.2020.08.120 Opening in a new tab
- URL
- https://www.sciencedirect.com/science/article/pii/S0020025520308860 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 200
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT5fe83f13c7a14b1e8b3f4b9e2098c2bd/
- URN
urn:pkr-prod:CUT5fe83f13c7a14b1e8b3f4b9e2098c2bd
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.