基于犹豫模糊语言术语集的正交模糊聚类算法

犹豫模糊语言术语集（Hesitance Fuzzy Linguistic Term Sets，HFLTSs）允许决策者们用几个可能的语言术语来评估一个属性.近来，采用HFLTSs来进行模糊聚类分析的问题越来越受关注.考虑到目前基于HFLTSs的模糊聚类算法还存在计算复杂度高的问题，提出了一种新的正交模糊聚类算法：首先计算样本之间的距离测度得到距离测度矩阵，接着计算其等价矩阵；然后确定置信水平值，通过置信水平值对等价矩阵进行切割；最后根据切割矩阵的列向量之间的正交关系来确定对应样本是否可以放在同一个类别，以此得到聚类结果.该算法步骤简单，计算复杂度低，并且适合于数据量大的模糊聚类问题.本文末尾将通过一个实例结合k-means聚类算法证明该算法的可行性和高效性.

Novel Orthogonal Fuzzy Clustering Algorithm Based on Hesitance Fuzzy Linguistic Term Sets

Hesitance Fuzzy Linguistic Term Sets (HFLTSs) allow decision makers to evaluate a property in several possible linguistic terms. Recently, HFLTSs based fuzzy clustering analysis draws increasing attention. Considering that the current fuzzy clustering algorithm based on HFLTSs still costs large computation, this study proposes a novel orthogonal fuzzy clustering algorithm. Firstly, calculate the distance measures between samples to construct distance measure matrix, and then calculate the matrix''s equivalent matrix. Secondly, cut the equivalent matrix according to its confidence level to obtain the corresponding cutting matrix. Finally, obtain the clustering result based on the orthogonal relationship between the column vectors of the cutting matrix. This algorithm has simple steps and low computational complexity. It is also suitable for large-scale fuzzy clustering problems. At last, the feasibility and efficiency of this algorithm are proved by a practical application with k-means clustering algorithm.