关键词: 公理模糊集结构, 公理模糊集代数, 聚类分析, 模糊集

Abstract: In the framework of AFS（Axiomatic Fuzzy Sets） theory，study a new clustering algorithm（FCA_AFS） and give a cluster validity index by which we can figure out the optimal number of clusters and the parameter values reaching maximal accurate rate.Compared with other clustering algorithms，the FCA_AFS algorithm can work out the cluster descriptions which are represented by some fuzzy sets with definitely semantic interpretations，and then every sample is clustered into the corresponding cluster according to the membership degrees belonging to the fuzzy sets.Not only has it avoided the complicated optimization problem that other fuzzy clustering algorithm have to resolve，but also the cluster number need not be given in advance.Evaluate the performance of the FCA_AFS algorithm using three well-known benchmark data sets—the Iris data，the Wine classification data，and Wisconsin breast cancer data to verify the clustering practicality and effectiveness.

Key words: Axiomatic Fuzzy Sets structure, Axiomatic Fuzzy Sets algebra, clustering analysis, fuzzy sets