第4期 张倩倩，等：基于关联熵系数的粗糙Vague集相似性度量方法 ·655· WANG Wei,PENG Jinye,LI Zhan.Covering rough Vague [18]苗夺谦，魏莱，徐菲菲.粗糙模糊集的关联嫡与关联嫡 sets and uncertainty measurement[J].Computer science, 系数.同济大学学报：自然科学版，2007,35(7)： 2012,39(8):228-232 970-974 [9]SUN Bingzhen,XU Youquan,ZENG Dalin.Rough Vague MIAO Duoqian,WEI Lai,XU Feifei.Relative entropy set over two universes[C]//Proceedings of 2013 Interna- and Its coefficient of rough fuzzy sets[J].Journal of tional Conference on Machine Learning and Cybernetics. Tongji university:natural science,2007,35(7):970-974. Tianjin,China,2013:682-686 [19]NAMBURU A.SAMAYAMANTULA S K.EDARA S [10]HUANG Bing,WEI Dakuan,LI Huaxiong,et al.Using a R.Generalised rough intuitionistic fuzzy c-means for rough set model to extract rules in dominance-based inter- magnetic resonance brain image segmentation[J].IET im- val-valued intuitionistic fuzzy information systems[J].In- age processing,.2017,11(9):777-785. formation sciences,2013,221:215-229. 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[23]刘鹏患.从模糊集到直觉模糊集相似度的构造方法)， GUO Yuting,LI Jinjin,LI Kedian,et al.Multi-granula- tion covering rough-intuitionistic fuzzy set model[J]. 西华大学学报：自然科学版，2016.35(2：17-24,87. Journal of Nanjing university:natural sciences,2015, LIU Penghui.Approaches to constructing similarity meas- 51(2:438-446. ures from fuzzy sets to intuitionistic fuzzy sets[J].Journal [14]范成礼，雷英杰，张戈.改进的直觉模糊粗糙集相似性 of Xihua university:natural science,2016,35(2):17-24, 度量方法).计算机应用，2011,31(5)：13441347. 87. FAN Chengli,LEI Yingjie,ZHANG Ge.Improved meas- 作者简介： ure of similarity between intuitionistic fuzzy rough 张倩倩，女，1982年生，实验师， sets[J].Journal of computer applications,2011,31(5): 主要研究方向为粗糙集，Vague集理 1344-1347. 论、粒计算。 [15]楚俊峰，王应明.基于新的区间直觉模糊集相似性测度 的模式识别[J1.计算机工程与应用，2013,49(9)： 140-143,155 CHU Junfeng,WANG Yingming.Method of pattern re- cognition based on new similarity measure of interval-val- ued intu-itionistic fuzzy set[J].Computer engineering and 马媛媛，女，1981年生，讲师，主 applications,.2013,49(9):140-143,155 要研究方向为粒计算、信息隐藏与多 [16]王毅，刘三阳，程月蒙，等.基于倾向性的直觉模糊相似 媒体安全。 度量方法[J].系统工程与电子技术，2015,37(4)： 863-867. WANG Yi,LIU Sanyang,CHENG Yuemeng,et al.Intu- itionistic fuzzy similarity measure approach based on ori- entation[J].Systems engineering and electronics,2015, 徐久成，男，1963年生，教授，博 37(4):863-867 士，主要研究方向为粗糙集、粒计算、 [17]权双燕，吴慧.Vague集的偏嫡与关联嫡[).计算机应 数据挖掘、生物信息。 用与软件，2008.25(2)：54-56. QUAN Shuangyan,WU Hui.Partial entropy and relative entropy of vague sets[J].Computer applications and soft- ware,2008.25(2):54-56WANG Wei, PENG Jinye, LI Zhan. Covering rough Vague sets and uncertainty measurement[J]. Computer science, 2012, 39(8): 228–232. SUN Bingzhen, XU Youquan, ZENG Dalin. Rough Vague set over two universes[C]//Proceedings of 2013 Interna￾tional Conference on Machine Learning and Cybernetics. Tianjin, China, 2013: 682–686. [9] HUANG Bing, WEI Dakuan, LI Huaxiong, et al. Using a rough set model to extract rules in dominance-based inter￾val-valued intuitionistic fuzzy information systems[J]. In￾formation sciences, 2013, 221: 215–229. [10] 郭庆, 杨善林, 刘文军. 直觉模糊集信息系统属性约简 算法[J]. 模糊系统与数学, 2014, 28(4): 138–143. GUO Qing, YANG Shanlin, LIU Wenjun. A novel attrib￾utes reduction algorithm of intuitionistic fuzzy-valued in￾formation system[J]. Fuzzy systems and mathematics, 2014, 28(4): 138–143. [11] HUANG Bing, GUO Chunxiang, ZHUANG Yuliang, et al. Intuitionistic fuzzy multigranulation rough sets[J]. In￾formation sciences, 2014, 277: 299–320. [12] 郭郁婷, 李进金, 李克典, 等. 多粒度覆盖粗糙直觉模糊 集模型[J]. 南京大学学报: 自然科学版, 2015, 51(2): 438–446. GUO Yuting, LI Jinjin, LI Kedian, et al. Multi-granula￾tion covering rough-intuitionistic fuzzy set model[J]. Journal of Nanjing university: natural sciences, 2015, 51(2): 438–446. [13] 范成礼, 雷英杰, 张戈. 改进的直觉模糊粗糙集相似性 度量方法[J]. 计算机应用, 2011, 31(5): 1344–1347. FAN Chengli, LEI Yingjie, ZHANG Ge. Improved meas￾ure of similarity between intuitionistic fuzzy rough sets[J]. Journal of computer applications, 2011, 31(5): 1344–1347. [14] 楚俊峰, 王应明. 基于新的区间直觉模糊集相似性测度 的模式识别[J]. 计算机工程与应用, 2013, 49(9): 140–143, 155. CHU Junfeng, WANG Yingming. Method of pattern re￾cognition based on new similarity measure of interval-val￾ued intu-itionistic fuzzy set[J]. Computer engineering and applications, 2013, 49(9): 140–143, 155. [15] 王毅, 刘三阳, 程月蒙, 等. 基于倾向性的直觉模糊相似 度量方法[J]. 系统工程与电子技术, 2015, 37(4): 863–867. WANG Yi, LIU Sanyang, CHENG Yuemeng, et al. Intu￾itionistic fuzzy similarity measure approach based on ori￾entation[J]. Systems engineering and electronics, 2015, 37(4): 863–867. [16] 权双燕, 吴慧. Vague 集的偏熵与关联熵[J]. 计算机应 用与软件, 2008, 25(2): 54–56. QUAN Shuangyan, WU Hui. Partial entropy and relative entropy of vague sets[J]. Computer applications and soft￾ware, 2008, 25(2): 54–56. [17] 苗夺谦, 魏莱, 徐菲菲. 粗糙模糊集的关联熵与关联熵 系数[J]. 同济大学学报: 自然科学版, 2007, 35(7): 970–974. MIAO Duoqian, WEI Lai, XU Feifei. Relative entropy and Its coefficient of rough fuzzy sets[J]. Journal of Tongji university: natural science, 2007, 35(7): 970–974. [18] NAMBURU A, SAMAYAMANTULA S K, EDARA S R. Generalised rough intuitionistic fuzzy c-means for magnetic resonance brain image segmentation[J]. IET im￾age processing, 2017, 11(9): 777–785. [19] LIU Yong, LIN Yi. Intuitionistic fuzzy rough set model based on conflict distance and applications[J]. Applied soft computing, 2015, 31: 266–273. [20] 刘金良, 闫瑞霞, 姚炳学. 粗糙 Vague 集的不确定性度 量[J]. 系统工程与电子技术, 2008, 30(1): 104–107. LIU Jinliang, YAN Ruixia, YAO Bingxue. Uncertainty measures in rough-vague set[J]. Systems engineering and electronics, 2008, 30(1): 104–107. [21] BORAN F E, AKAY D. A biparametric similarity meas￾ure on intuitionistic fuzzy sets with applications to pat￾tern recognition[J]. Information sciences, 2014, 255: 45–57. [22] 刘鹏惠. 从模糊集到直觉模糊集相似度的构造方法[J]. 西华大学学报: 自然科学版, 2016, 35(2): 17–24, 87. LIU Penghui. Approaches to constructing similarity meas￾ures from fuzzy sets to intuitionistic fuzzy sets[J]. Journal of Xihua university: natural science, 2016, 35(2): 17–24, 87. [23] 作者简介： 张倩倩，女，1982 年生，实验师， 主要研究方向为粗糙集、Vague 集理 论、粒计算。 马媛媛，女，1981 年生，讲师，主 要研究方向为粒计算、信息隐藏与多 媒体安全。 徐久成，男，1963 年生，教授，博 士，主要研究方向为粗糙集、粒计算、 数据挖掘、生物信息。 第 4 期 张倩倩，等：基于关联熵系数的粗糙 Vague 集相似性度量方法 ·655·