Focusing on 10 typical rural tourism scenic spots in different cities in Shanxi province, we construct an index system of the rural tourism public service. Constituted through the data of two questionnaires is a third-order tensor of ``surveyed tourists $\times$ survey indicators $\times$ scenic spots". Using the high precision low rank tensor (matrix) algorithm to fill missing data, we then use the Fmincon function to calculate the weights for the five most important indexes in scenic spots and satisfaction and overall satisfaction scores. The analyses show that tourists are generally dissatisfied with the self-guided tour service, and the satisfaction is significantly lower than its importance. Tourists' satisfaction and attention to theatrical performances are low. Tourists are significantly more satisfied with the information about safety risks than they take seriously. We should improve the shortcomings of tourism public services from a small point and continue to increase investment in rural tourism public services.