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 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.