With regarding to the multi-attribute group decision-making problem of the triangular fuzzy number  (TFN) with the attribute weights and experts weights being unknown, the confidence index is constructed based on the TFN entropy to quantify the degree of certitude to the decision information, and the TFN certitude degree (TFNCD) operator is introduced and its properties, such as the invariance of displacement transformation,  the idempotence and the boundedness are proved. And the expert weights are determined combined with the degree of support. Finally, a method of attribute information aggregation is proposed, and the effectiveness of the TFNCD operator and the aggregated approach are verified by the empirical analysis. Moreover, the approach is built on the independence of experts, where the data features of the TFNs and the completely unknown weights of attributes and experts are fully considered, resulting in the objectivity and high efficiency in the information aggregation with relatively reduced computation. Therefore, it provides an information aggregation mode and solution to the multi-attribute group decision-making problem with TFN.