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Driven by the development of platform economy, two-sided matching decision-making (TSDM) has become one of the most important applications in the field of intelligent computation system. Many recommendation systems based on TSDM have facilitated our life. However, in the existing studies on TSDM, it is usually assumed that all the individuals provide their preference orderings accurately, and have the same stable demand. In this paper, we develop an optimization method to solve the TSDM problem with incomplete weak preference ordering and heterogeneous fuzzy stable demand (i.e., TSDM-IH method). First, based on the incomplete weak preference ordering by the individuals in the two-sided matching party, we calculate the expectation ordinal values for each individual. Then, we calculate the perceived difference matrices and the perceived value matrices for the individuals in the two-sided matching party. Next, we analyze the fuzzy expression on the fuzzy stable demand for each individual, and obtain the constraint for obtaining the stable alternatives. Furthermore, we develop an optimization model which maximizes the perceived values of individuals in the two-sided matching party. Finally, a numerical example is given to illustrate the feasibility of the TSDM-IH method.