犹豫模糊信息下的协相关度与聚类分析  

Co-correlation Degree under Hesitant Fuzzy Information and Clustering Analysis

作　　者：汪峰[1] 毛军军[1,2] 祖璇 邹斌[4] WANG Feng;MAO Junjun;ZU Xuan;ZOU Bin(School of Mathematical Sciences,Anhui University,Hefei 230601,China;Key Lab of Intelligent Computing&Signal Processing of Ministry of Education,Anhui University,Hefei 230039,China;Department of Economics,Wanjiang College of Anhui Normal University,Wuhu,Anhui 241008,China;School of Educational Science,Anhui Radio and TV University,Hefei 230022,China)

机构地区：[1]安徽大学数学科学学院,合肥230601 [2]安徽大学计算智能与信号处理教育部重点实验室,合肥230039 [3]安徽师范大学皖江学院经济系,安徽芜湖241008 [4]安徽广播电视大学教育科学学院,合肥230022

出　　处：《计算机科学与探索》2018年第5期828-838,共11页Journal of Frontiers of Computer Science and Technology

基　　金：国家自然科学基金No.61673020;2016年高校优秀青年人才支持计划重点项目No.gxyq ZD2016453;安徽省高等学校自然科学基金重点项目No.KJ2017A945;安徽大学研究生创新项目No.yfc100020~~

摘　　要：针对决策信息为犹豫模糊集且属性权重完全未知的多属性聚类问题,提出了一种基于犹豫模糊交叉熵的协相关度与聚类方法。为区分不同的犹豫模糊集,定义了犹豫模糊元的交叉熵,通过与其他距离公式得出的结果进行对比,验证了它的有效性与合理性;由犹豫模糊交叉熵公式,按照离差最大化算法得出属性权重公式;然后提出犹豫模糊集协相关度的概念,证明了它与传统相关系数类似的性质,并将协相关度公式加权;最后把加权的协相关度公式用于犹豫模糊信息下的聚类分析中,通过比较分析不同文献的聚类结果,验证了所提聚类算法的可行性与有效性。For the multi-attribute clustering problem that decision information is hesitant fuzzy set(HFS)and the attribute weights are completely unknown,this paper proposes a co-correlation degree based on hesitant fuzzy crossentropy and clustering method.In order to distinguish different HFSs,this paper defines the cross-entropy between two hesitant fuzzy elements(HFEs),and verifies the validity and rationality in comparison with the results obtained by other distance formulas.Next,this paper derives the formula of attribute weights according to the maximizing deviation algorithm from the hesitant fuzzy cross-entropy.Then,this paper proposes the concept of co-correlation degree,proves its similar properties with the traditional correlation coefficient,and considers different attributes??weight at the same time,which is determined by the formula of attribute weights.Finally,this paper uses the weighted formula of co-correlation degree for clustering analysis under hesitant fuzzy information,and verifies the feasibility and effectiveness through the comparison analysis of clustering results of diverse literature.

关 键 词：犹豫模糊集 交叉熵 离差最大化 协相关度 聚类分析 

分 类 号：C934[经济管理—管理学]