To solve the cloud service supplier selection problem under the background of cloud computing emergence, an integrated group decision method is proposed. The cloud service supplier selection index framework is built from two perspectives of technology and technology management. Support vector machine- (SVM-) based classification model is applied for the preliminary screening to reduce the number of candidate suppliers. A triangular fuzzy number-rough sets-analytic hierarchy process (TFN-RS-AHP) method is designed to calculate supplier’s index value by expert’s wisdom and experience. The index weight is determined by criteria importance through intercriteria correlation (CRITIC). The suppliers are evaluated by the improved TOPSIS replacing Euclidean distance with connection distance (TOPSIS-CD). An electric power enterprise’s case is given to illustrate the correctness and feasibility of the proposed method.