Uncertainty representation of grey numbers and grey sets

Yang, Yingjie; Liu, Sifeng; John, Robert

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.

Citation

Yang, Y., Liu, S., & John, R. (2014). Uncertainty representation of grey numbers and grey sets. IEEE Transactions on Cybernetics, 44(9), https://doi.org/10.1109/TCYB.2013.2288731

• Journal Article Type: Article
• Publication Date: Aug 14, 2014
• Deposit Date: Sep 27, 2014
• Publicly Available Date: Sep 27, 2014
• Journal: IEEE Transactions on Cybernetics
• Electronic ISSN: 2168-2275
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 44
• Issue: 9
• DOI: https://doi.org/10.1109/TCYB.2013.2288731
• Keywords: Grey sets, Fuzzy sets, Relative uncertainty
• Public URL: https://nottingham-repository.worktribe.com/output/734219
• Publisher URL: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6668878
• Additional Information: © 2013 IEEE.