An axiomatic definition for the degree of greyness of grey numbers

In this paper, an axiomatic system for defining the degree of greyness of grey numbers is built based on discussion with two definitions of degree of greyness of grey numbers. Then, the axioms can be taken as a criterion for defining the degree of greyness of grey numbers, a new formula for the degree of greyness of grey numbers with a measure of the true range of a grey number and the background or field which the grey number is brought about. Lastly, the degree of uncertainty of a grey number is described scientifically, and some problems existing in old definitions have been overcome in this new definition. The greyness theory and the whitenization of grey number is the foundation of the grey systems theories, and the contribution of this paper is helpful to its growth well.