Grey-incidence clustering decision-making method with three-parameter interval grey number based on regret theory

Aiming at the multiple attribute decision making problem with three-parameter interval grey numbers, a grey-incidence clustering decision making method based on regret theory is proposed in this paper. First, according to the idea of TOPSIS method, a kind of comprehensive grey interval incidence coefficient of three-parameter interval grey number is defined, and the “regret-rejoice” value is calculated out based on the grey interval relational coefficients, so the grey relational comprehensive perceptional utility of decision attribute value is obtained by adding the perceptive utility value of comprehensive grey interval incidence coefficient. Then, differing from the traditional grey-incidence clustering method, in this paper, grey clustering analysis is proceeded on the basis of the calculated matrix of comprehensive perceptional utility, so the comprehensive clustering results are achieved, and the ranking of the alternatives which are included in one class can be achieved too. Finally, the rationality and validity of the proposed method are verified by comparison analysis with an example.