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This paper employs the possibility-satisfiability method which has been widely recognized in the field of social-economic decision-making. In order to further improve the accuracy of decision-making, it also innovatively introduces the method of support vector machines based on the chaotic time series. This method is used to predict the high point and the low point of the index in the possibility-satisfiability algorithm. Then the paper uses this model with the optimal full coverage time decision of the new type of rural social endowment insurance system in 20 central and western provinces in China as a case study. Meanwhile, the empirical research is also conducted in this paper and the results show that this model has provided a good decision support.