以山西省各地市10个典型乡村旅游景区为对象，构建了乡村旅游公共服务指标体系，通过两次问卷调查所得数据构成“被调查人员$\times$调查指标$\times$景区”的三阶张量，利用高精度低秩张量(矩阵)算法先对缺失数据进行填充，而后利用Fmincon函数计算出每个景区5项最重要指标的权重和满意度分值及总体满意度分值。分析可知，游客普遍对自助导游服务不满意，且满意度明显低于重视度；对文艺演出活动的满意度和重视程度都偏低；对安全风险信息提示的满意度明显高于重视程度。为此，应从细微处改善旅游公共服务短板，并持续增加乡村旅游公共服务投入。

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.