Research on evaluations of several grey relational models adapt to grey relational axioms

Grey relational analysis is an important part of the grey systems theory, and it is the basis of the grey clustering analysis, grey decision-making and grey controlling. To research whether grey relational models satisfy the four grey relational theorems, several kinds of grey relational models are commented. Some problems including the properties of normality, pair symmetry and wholeness are discussed. The phenomenon that the lower value of almost each grey relational model is not equal to zero is proved. The contradiction problems between the properties of wholeness and pair symmetry are verified. Finally, several propositions are constructed to explain the above problems.