The fuzzy number is a special case of fuzzy set. As a generalization of the fuzzy num- ber, trapezoidal intuitionistic fuzzy number (TrIFN) is a special intuitionistic fuzzy set defined on the real number set, which seems to suitably describe an ill-known quantity. The purpose of this paper is to propose a new method for solving the multi-attribute group decision making problems, in which the attribute values are TrIFNs and the attribute weight information are incomplete. The concepts, such as the weighted lower and upper possibility means, the weighted possibility means and variances of TIFNs, are introduced. Hereby, a new lexicographic method is developed to rank the TrIFNs. In the proposed method, the weights of experts are determined in terms of the voting model of intuitionistic fuzzy set. The attribute weights are objectively derived through construct- ing the bi-objective programming model, which is transformed into the single objective quadratic programming model to solve. The ranking order of alternatives is generated by the collective over- all attribute values of alternatives. The stock selection example and comparison analyzes show the validity and applicability of the method proposed in this paper.