Using the concept of support degree in rough set theory for reference, two new concepts, namely dominant support degree and recessive support degree were proposed in this paper. By utilizing these new concepts, two simple weight assignment methods by which dominant weight and recessive weight of attributes could be obtained. Nonetheless both the methods had drawbacks. Hence a further method was developed below. The first step was to construct two items of evidence by deploying dominant weights vector and recessive weights vector of the attribute set and then assigned weights for the evidence to construct weighted evidence. Next was to combine the two items of weighted evidence in reference to the D-S evidential theory. Finally the weight assignments for the attributes could be procured after further processing the combination result. Furthermore, the concept of joint dominant weight of multiple attributes and related methods to assign weights for attributes in some particular situations were proposed. The rationality and wide scope of application of above methods were proven.