Abstract: In order to reveal the mathematical mechanism of generating grey numbers and the law of grey number evolution, the extension principle of grey set is proposed in this paper firstly, which provides a theoretical basis for grey number operation. Secondly, based on the possibility function of grey set, the concept and properties of grey convex set are given. According to grey convex set, the definitions of grey real number, universal grey real number and interval grey number are put forward. Thirdly, the basic operation rules of grey real number are given based on the extension principle, and the operations of data block expression are further given to meet the reversibility of grey real number operation. Finally, the sufficient and necessary condition for the reversibility of universal grey real number operation is given, and it is proved that the grey real number operations using data block expression are reversible. Examples show that the grey real number operations using data block expression proposed in this paper are feasible and effective. The research results enrich the grey system theory and provide a theoretical basis for grey algebra research.  

Key words: Grey real number, Universal grey real number, Interval grey number, Operation rules, Data block expression