Hybrid grey multiple attribute decision-making method with partial weight information

The hybrid grey attribute decision-making problem that the attribute weights are partially known is discussed, in which the attribute values are interval grey numbers and linguistic grades, and a new method based on evidential reasoning(ER) is proposed. The method is that decision-maker gives whitenization of each interval grey number based on his/her preference and belief structure form of qualitative attribute values, whitenization of quantitative attribute can be equivalently expressed in the form of belief structure with the principle of utility value equivalence, and then grade belief structure decision matrix can be determined. By using the analytical ER algorithm, belief degrees of each alternative belonging to each linguistic grade are obtained. Two pairs of nonlinear optimization models which are solved by genetic algorithms (GA) are constructed to compute the maximum and the minimum expected utilities of each alternative, respectively. Expectation-variance method for ranking interval numbers is utilized to rank the alternatives. A numerical example is used to show the feasibility and effectiveness of the proposed method.