Abstract: In order to quantitatively describe the grey properties of grey set, based on the possibility function of grey set, this paper discusses the expression method of the greyness of grey set and its applications. Firstly, the axiomatic definition and a method of calculating the greyness of grey set are given, and its rationality is analyzed through examples. Then, according to the principle of unity of opposites, the concept of whiteness of grey set is given, and the applications of greyness of grey set are analyzed. Finally, some examples are given to verify the validity of greyness of grey set and its application model. The results show that the axiomatic definition of greyness of grey set not only conforms to the grey immortal axiom, but also can quantitatively describes the dynamic evolution state of grey hazy set (grey set). The application examples show that the grey relational degree model and the grey decision model based on the greyness of grey set are feasible and effective. The research results not only enrich the theory of grey mathematics and grey system, but also provide a new method for grey relational analysis and grey decision.  

Key words: Grey set, Possibility degree, Greyness of grey set, Whiteness of grey set, Grey decision