The multi-granular probabilistic linguistic asymmetric normal cloud(MPLANC) two-sided matching decision making method is proposed based on cumulative prospect theory, which is to solve the two-sided matching problem with the issue of information loss in multi-granular probabilistic linguistic sets and failure to consider the psychological behavior of agents. Firstly, the MPLANC and its possibility degree are defined for solving and comparing multi-granular probabilistic linguistic information, which is both simple and effective while minimizing the loss of raw information. Meanwhile, the nonlinear optimization model based on the MPLANC bidirectional projection and the MPLANC power Heronian mean(HM) aggregation operator are constructed to obtain the attribute weights for different agents and positive and negative ideal reference points respectively. Then, the prospect value matrix of two-sided agents is developed based on the cumulative prospect theory to reflect the psychological behavior of two-sided agents. A multi-objective optimization model is constructed based on maximizing prospect values to obtain the optimal matching result. Finally, an example on service outsourcing matching is provided to verify the effectiveness and practicality of the proposed method, and the flexibility and advantages of the proposed method are further demonstrated by sensitivity analysis and comparative analysis.