The determination of weight vectors is the key problem for multiple attribute decision making. The linear combination weighting is an effective way to do it. The general description of the linear combination weighting problem is provided. Based on the information used to solve the problem, the solution methods are classified as four different classes. The fundamental idea for each class is demonstrated. The characteristics of each class are analyzed. This is useful to understand the different methods, and can provide references to the practical use of the methods.