An Improved Test Method for Grey Relational Order

It is impossible to obtain all the information of a decision-making problem in reality, so uncertain decision-making is very important in decision-making theory. Fuzzy mathematics, stochastic programming, interval analysis and grey system theory are generally used to deal with those uncertain decision-making problems. Grey relational analysis (GRA) is one of the elements of grey system theory. Grey relational grade (GRG) is the mean value of a series of grey relational coefficients in GRA, it may be inappropriate that GRGs are directly ranked without significant test. In this paper, we first present some common methods to deal with uncertain decision-making, then review the use and development of GRA, and propose their common drawback. Secondly, generalized GRG is introduced on the basic of mean value and standard deviation. Thirdly, an improved test method for grey relational order based on generalized GRG and probability distribution are proposed. Then, a set of formula has been derived to calculate the power of GRA. Finally, an example is investigated to demonstrate the use of the presented method in grey relational order test.