Abstract: Based on grey system theory,the grey attribute group decision-making problem is discussed,in which the attribute values are interval grey numbers and the attribute weights and authoritative weights are unknown. The concepts of individual imagined optimum vector,ideal expert,and predominance strength and predominance comparative matrix in the alternatives are presented by using analytical techpique. According to essentials of interval grey number,a new definition of deviation degree between two interval grey numbers is given,and an incidence degree coefficient formula based on deviation degree for interval grey numbers is constructed. Two algorithms that are the eigenvector method based on projection and priority method of fuzzy complementary judgment matrix for this grey group decision-making are presented,in which attribute weights and authoritative weights of decision-makers are unknown. These algorithms avoid the calculation of attribute weights and authoritative weights. An example shows the rationality of grey attribute group decision-making method and the validity of the algorithms mentioned above.

Key words: interval grey number, grey incidence degree, ideal expert, eigenvector, fuzzy complementary judgment matrix, eigenvector, group decision-making