Abstract: In order to solve the decision-making problem that the attributive values are internal grey numbers and the attributive weights are unknown, this paper try to construct an entropy-weighted TOPSIS model based on the generalized greyness of interval grey number from the perspectives of proximity and equilibrium. Firstly, the properties of greyness distance are analyzed and the simplified formula for computing greyness distance is given. Then, a method to determine entropy weight based on greyness distance is given, and an entropy weighted TOPSIS decision-making model is established. Finally, the constructed model is applied to selecting brackish water irrigation pattern of winter wheat in North China Plain, China, so to verify its feasibility and effectiveness. The results show that the model proposed in this paper not only fully utilizes the measurement information of interval grey numbers, but also overcomes the influence of subjective factors on weights, and provide a new method for decision-making of unknown attributive weights and attributive value with interval grey number, and the interval grey numbers coexist with the real numbers. The application examples show that the model proposed in this paper is feasible and valid. 

Key words: Interval grey number , Generalized greyness , Greyness distance ,  , Entropy-weighted TOPSIS model