This study presents a total integral value based fuzzy multiple criteria decision making (MCDM) approach for evaluating suppliers, where the membership function of the final fuzzy evaluation value of each alternative can be developed and the procedure for ranking these final fuzzy evaluation values can be clearly formulated based on total integral value to facilitate efficient decision making. The suggested approach assesses the ratings of alternatives versus subjective criteria and the importance weights of all criteria using linguistic values represented by triangular fuzzy numbers. A method based on t-score probability is suggested to normalize the suitability values of alternatives versus objective criteria. The proposed method preserves the property that the range of normalized values under quantitative criteria belongs to [0,1]. Finally, a numerical example of the evaluation and selection of suppliers is presented to demonstrate the computational process and feasibility of the proposed approach.