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The grey multiple attribute decision-making problem with preference information on alternatives is discussed in this paper, in which the attribute values are interval grey numbers and the attribute weights unknown, and the algorithms for this grey decision-making is presented. According to essentials of interval grey number, definition of deviation degree between two interval grey numbers is given, and an incidence degree coefficient formula and relative incidence degree coefficient formula based on deviation degree for interval grey numbers are constructed by using analytical technique. For the attribute weights unknown, this paper introduces the optical model of minimum deviation method based on deviation between objective preference and subjective for making the attribute weights. The method can sufficiently utilize objective information , and meet decision-maker's subjective requirement, and can be easily performed on computer. An example shows the rationality of grey incidence decision-making and the validity of the algorithms mentioned above.