Abstract: The two-sided matching has been widely applied to the decision-making problems in the field of management. With the limited working experience, the two-sided agents usually cannot provide the preference order directly for the opposite agent, but rather to provide the preference relations in the form of linguistic information. The preference relations based on probabilistic linguistic term sets (PLTSs) not only allow agents to provide the evaluation with multiple linguistic terms, but also present the different preference degrees for linguistic terms. Considering the diversities of the agents, they may provide their preference relations in the form of the probabilistic linguistic preference relation (PLPR) or the probabilistic linguistic multiplicative preference relation (PLMPR). For two-sided matching with the expected time, we first provide the concept of the time satisfaction degree (TSD). Then, we transform the preference relations in different forms into the unified preference relations (u-PRs). The consistency index to measure the consistency of u-PRs is introduced. Besides, the acceptable consistent u-PRs are constructed, and an algorithm is proposed to modify the unacceptable consistent u-PRs. Furthermore, we present the whole two-sided matching decisionmaking process with the acceptable consistent u-PRs. Finally, a case about aviation technology suppliers and demanders matching is presented to exhibit the rationality and practicality of the proposed method. Some analyses and discussions are provided to further demonstrate the feasibility and effectiveness of the proposed method.

Key words: Two-sided matching, Time satisfaction degree, Probabilistic linguistic term sets, Preference relation, Aviation technology