In view of the fact that most clustering algorithms cannot solve the clustering problem about samples with uncertain information, according to the theory of fuzzy sets and probability, we define the fuzzy-probability binary measure space and triangular fuzzy normal random variables firstly, and then combine the advantages of k-means algorithm, such as simple principle, few parameters, fast convergence rate, good clustering effect and good scalability, etc., a clustering algorithm is proposed for samples containing multiple triangular fuzzy normal random variables, which we call TFNRV-k-means algorithm. The algorithm uses our proposed Euclidean random comprehensive absolute distance (ERCAD for short) as a measurement, under the fuzzy measure, the lower bound, the principal value and the upper bound of the triangular fuzzy normal random variables are iterated, respectively, by means, and then the cluster center is updated until it becomes stable and unchanged. Then we analyze the time complexity of the proposed algorithm, and test the algorithm under different sample sets by random simulation experiments. We get the highest clustering accuracy of 99.00% and the maximum Kappa coefficient of 0.9850, and draw the conclusion that TFNRV-k-means clustering algorithm has good clustering effect. Finally, we summarize the content of the article, list the advantages and disadvantages of TFNRV-k-means clustering algorithm, and propose corresponding improvement methods, which provide ideas for further research on TFNRV-k-means in the future.

鉴于大多数聚类算法无法解决信息不确定的样本的聚类问题，根据模糊集和概率理论，首先定义了模糊概率二元测度空间和三角模糊正态随机变量，然后结合针对k均值算法的优点，如原理简单，参数少，收敛速度快，聚类效果好，可扩展性好等优点，针对包含多个三角模糊正态随机变量的样本提出了一种聚类算法，称为TFRNV- ķ-均值算法。该算法使用我们提出的欧几里德随机综合绝对距离（简称ERCAD）作为度量，在模糊度量下，分别通过以下方式迭代三角模糊正态随机变量的下界，主值和上界：然后更新集群中心，直到它变得稳定和不变。然后，分析了该算法的时间复杂度，并通过随机仿真实验在不同样本集下对该算法进行了测试。我们得到了最高的聚类精度为99.00％，最大Kappa系数为0.9850，得出的结论是TFNRV- k -means聚类算法具有良好的聚类效果。最后，我们总结了本文的内容，列出了TFNRV-的优缺点k -means聚类算法，并提出相应的改进方法，为今后进一步研究TFNRV- k -means提供了思路。