Uncertainty representation of grey numbers and grey sets
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 r...
| Main Authors: | , , |
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| Format: | Article |
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IEEE
2014
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| Online Access: | https://eprints.nottingham.ac.uk/3369/ |
| _version_ | 1848791024120365056 |
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| author | Yang, Yingjie Liu, Sifeng John, Robert |
| author_facet | Yang, Yingjie Liu, Sifeng John, Robert |
| author_sort | Yang, Yingjie |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:21:56Z |
| format | Article |
| id | nottingham-3369 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:21:56Z |
| publishDate | 2014 |
| publisher | IEEE |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-33692020-05-04T16:52:30Z https://eprints.nottingham.ac.uk/3369/ Uncertainty representation of grey numbers and grey sets Yang, Yingjie Liu, Sifeng John, Robert 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. IEEE 2014-08-14 Article PeerReviewed Yang, Yingjie, Liu, Sifeng and John, Robert (2014) Uncertainty representation of grey numbers and grey sets. IEEE Transactions on Cybernetics, 44 (9). pp. 1508-1517. ISSN 2168-2267 Grey sets Fuzzy sets Relative uncertainty http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6668878 doi:10.1109/TCYB.2013.2288731 doi:10.1109/TCYB.2013.2288731 |
| spellingShingle | Grey sets Fuzzy sets Relative uncertainty Yang, Yingjie Liu, Sifeng John, Robert Uncertainty representation of grey numbers and grey sets |
| title | Uncertainty representation of grey numbers and grey sets |
| title_full | Uncertainty representation of grey numbers and grey sets |
| title_fullStr | Uncertainty representation of grey numbers and grey sets |
| title_full_unstemmed | Uncertainty representation of grey numbers and grey sets |
| title_short | Uncertainty representation of grey numbers and grey sets |
| title_sort | uncertainty representation of grey numbers and grey sets |
| topic | Grey sets Fuzzy sets Relative uncertainty |
| url | https://eprints.nottingham.ac.uk/3369/ https://eprints.nottingham.ac.uk/3369/ https://eprints.nottingham.ac.uk/3369/ |