Study on affine property of some algorithms for grey relational analysis

The grey relational analysis is an important branch of grey system theory. It is the foundation of grey clustering, decision-making, and control. The aim of this paper is to further study the properties of algorithms for grey relational analysis. On the basis of analysis on the existing models for grey relational analysis and their properties, this paper first presents the novel definition of affinity for grey relational model. Secondly, the affine property of some models for grey relational analysis is studied. Finally, the study result indicates that the algorithm for grey T-mode relational analysis and the algorithm for grey rate relational analysis are of affinity. This result may enrich the theoretical system of grey relational analysis.