With respect to the two-sided matching problems with intuitionistic fuzzy preference information, in which the reference dependence and loss aversion psychological behavior of the agents are considered, a two-sided fair and satisfied matching method is proposed based on TODIM (TOmada de decis\ao interativa multicritério). Firstly, the description of two-sided matching problems with intuitionistic fuzzy preference information is given. Then, the intuitionistic fuzzy preference information of the agents on both sides are transformed in to the gains or losses relative to the reference point based on the prospect theory. Furthermore, the total dominance degree of each agent is calculated based on the TODIM method, and the calculating rules of satisfaction degree is confirmed. An optimization two-sided fair and satisfied matching model is constructed, and the two-sided matching result can be obtained by solving the model. Finally, an example is given to prove the feasibility and validity of the proposed method.