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...

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Bibliographic Details
Published in:IEEE transactions on cybernetics 2014-09, Vol.44 (9), p.1508-1517
Main Authors: Yingjie Yang, Sifeng Liu, John, Robert
Format: Article
Language:English
Subjects:
Computer science
Cybernetics
Educational institutions
Equivalence
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy sets
grey sets
Measurement uncertainty
relative uncertainty
Representations
Rough sets
Uncertainty
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Summary: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 analyzed from the point of view of the proposed uncertainty representation. The analysis demonstrates that grey sets and interval-valued fuzzy sets provide different but overlapping models for uncertainty representation in sets.
ISSN:2168-2267
2168-2275
DOI:10.1109/TCYB.2013.2288731