Skip to main content

Research Repository

Advanced Search

Uncertainty representation of grey numbers and grey sets

Yang, Yingjie; Liu, Sifeng; John, Robert

Authors

Yingjie Yang yyang@dmu.ac.uk

Sifeng Liu sfliu@nuaa.edu.cn

Robert John robert.john@nottingham.ac.uk



Abstract

In the literature there is a presumption that a grey set and
an interval-valued fuzzy set are equivalent. This presumption ignores the existence of discrete components in a grey number. In this paper new measurements of uncertainties of grey numbers and grey sets,
consisting of both absolute and relative uncertainties, are defined to give a comprehensive representation of uncertainties in a grey number and a grey set. Some simple examples are provided to illustrate that the proposed uncertainty measurement can give an effective representation of both absolute and relative uncertainties in a grey number and a grey set. The relationships between grey sets and interval-valued fuzzy sets are also analysed from the point of view of the proposed uncertainty representation. The analysis demonstrates that grey sets and intervalvalued fuzzy sets provide different but overlapping models for uncertainty
representation in sets.

Journal Article Type Article
Publication Date Aug 14, 2014
Journal IEEE Transactions on Cybernetics
Electronic ISSN 2168-2267
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 44
Issue 9
APA6 Citation Yang, Y., Liu, S., & John, R. (2014). Uncertainty representation of grey numbers and grey sets. IEEE Transactions on Cybernetics, 44(9), doi:10.1109/TCYB.2013.2288731
DOI https://doi.org/10.1109/TCYB.2013.2288731
Keywords Grey sets, Fuzzy sets, Relative uncertainty
Publisher URL http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6668878
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information © 2013 IEEE.

Files

grey_uncertainty_ieee_07.pdf (310 Kb)
PDF

Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





You might also like



Downloadable Citations

;