Based on a multi-valued mapping from a probability space (X,(Omega) ,Rmu) to space S, a probability measure over a class 2s of subsets of S is defined. Then using the product combination rule of multiple information sources, the Dempster-Shafer combination rule is derived. The investigation of the two rules indicates that the Dempster rule and the Dempster-Shafer combination rule are for different spaces. Some problems of the Dempster-Shafer combination rule are interpreted via the product combination rule that is used for multiple independent information sources. A technique to improve the method is proposed. Finally, an error in multi-valued mappings in  is pointed out and proved.