Uncertainty Representation of Grey Numbers and Grey Sets

Abstract

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.

Predicting construction cost under uncertainty using grey-fuzzy earned value analysis

“…The degree of greyness ( is determined as shown in Eq. (8) [ 25 , 57 ]. Where: L : Lower Limit of grey number; U : Upper Limit of grey number; : Minimum Value of the grey number domain; : Maximum Value of the grey number domain; , .…”

Application of Pfahp-Gtopsis Methods for Third-Party Logistics Provider Selection

“…Fuzzy set theory and grey set theory may be employed to deal with the imprecision and vagueness of decision-makers. Therefore, both fuzzy set theory (Zadeh, 1978;Zadeh et al, 1996) and grey set theory (Yang et al, 2013;Yang & John, 2012) were implemented for the 3PLP selection problem. The integration of these sets has not been presented to the best of the authors' knowledge for 3PLP selection.…”

“…As an extension of fuzzy sets, grey sets can be studied if the values of their characteristic functions are restricted to the interval (Yang & John, 2012). Additionally, some researchers believe grey sets are the generalization of an interval-valued fuzzy set (Khuman et al, 2014;Yang et al, 2013). Instead of expressing the people's preference for crisp numbers, a wider scope of the number may be established via intervals.…”