[1]ZHANG Qianqian,MA Yuanyuan,XU Jiucheng.Measurement method of the similarity of rough vague sets based on relative entropy coefficient[J].CAAI Transactions on Intelligent Systems,2018,13(4):650-655.[doi:10.11992/tis.201706081]
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Measurement method of the similarity of rough vague sets based on relative entropy coefficient

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 13 Number of periods: 2018 4 Page number: 650-655 Column: 学术论文—人工智能基础 Public date: 2018-07-05
Title:
Measurement method of the similarity of rough vague sets based on relative entropy coefficient
Author(s):
ZHANG Qianqian1; 2; 3;  MA Yuanyuan1; 2; 3;  XU Jiucheng1; 2; 3
1. College of Computer and Information Technology, Henan Normal University, Xinxiang 453007, China;
2. Engineering Lab of Intelligence Business & Internet of Things, Xinxiang 453007, China;
3. Engineering Technology Research Center for Computing Intelligence & Data Mining, Henan Province, Xinxiang 453007, China
Keywords:
rough Vague set; similarity measure; relative entropy; relative entropy coefficient; rough set
CLC:
TP18
DOI:
10.11992/tis.201706081
Abstract:
The rough Vague set is a theoretical tool that combines the theories of rough and Vague sets to deal with uncertain information. In this paper, we introduce the concept of relative entropy and its coefficient to a rough Vague set to investigate a method for measuring relative entropy, its coefficient, and the similarity of Vague and rough fuzzy sets. We also analyzed their main properties. We verified that the coefficient of the relative entropy has similarity with that of rough Vague sets, and that this coefficient can be used to measure the similarity of rough Vague sets. Finally, we conducted a case study to verify the effectiveness of using the relative entropy coefficient of a rough Vague set to determine the degree of similarity between rough Vague sets. This theory provides a new method for measuring the similarity of rough Vague sets.
References:
[1] PAWLAK Z. Rough sets:theoretical aspects of reasoning about data[M]. Dordrecht, Netherlands:Kluwer Academic Publishers, 1991.
[2] GAU W L, BUEHRER D J. Vague sets[J]. IEEE transactions on systems, man, and cybernetics, 1993, 23(2):610-614.
[3] ZHANG Qingchuan, ZENG Guangping, XIAO Chaoen, et al. A rule conflict resolution method based on Vague set[J]. Soft computing, 2014, 18(3):549-555.
[4] 欧阳春娟, 李斌, 李霞, 等. 基于Vague集相似度量的图像隐写系统安全性测度[J]. 计算机学报, 2012, 35(7):1510-1521. OUYANG Chunjuan, LI Bin, LI Xia, et al. A new security evaluation for steganographic system based on vague set similarity measure[J]. Chinese journal of computers, 2012, 35(7):1510-1521.
[5] ATANASSOV K T. Intuitionistic fuzzy sets[J]. Fuzzy sets and systems, 1986, 20(3):87-96.
[6] BUSTINCE H, BURILLO P. Vague sets are intuitionistic fuzzy sets[J]. Fuzzy sets and systems, 1996, 79(3):403-405.
[7] 徐久成, 张倩倩. 覆盖粗糙Vague集的不确定性度量研究[J]. 计算机科学, 2010, 37(10):225-227, 282. XU Jiucheng, ZHANG Qianqian. Research on uncertainty measurement for covering rough-vague sets[J]. Computer science, 2010, 37(10):225-227, 282.
[8] 王伟, 彭进业, 李展. 一种覆盖粗糙Vague集模型及其不确定性度量[J]. 计算机科学, 2012, 39(8):228-232. WANG Wei, PENG Jinye, LI Zhan. Covering rough vague sets and uncertainty measurement[J]. Computer science, 2012, 39(8):228-232.
[9] SUN Bingzhen, XU Youquan, ZENG Dalin. Rough Vague set over two universes[C]//Proceedings of 2013 International Conference on Machine Learning and Cybernetics. Tianjin, China, 2013:682-686.
[10] HUANG Bing, WEI Dakuan, LI Huaxiong, et al. Using a rough set model to extract rules in dominance-based interval-valued intuitionistic fuzzy information systems[J]. Information sciences, 2013, 221:215-229.
[11] 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 attributes reduction algorithm of intuitionistic fuzzy-valued information system[J]. Fuzzy systems and mathematics, 2014, 28(4):138-143.
[12] HUANG Bing, GUO Chunxiang, ZHUANG Yuliang, et al. Intuitionistic fuzzy multigranulation rough sets[J]. Information sciences, 2014, 277:299-320.
[13] 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-granulation covering rough-intuitionistic fuzzy set model[J]. Journal of Nanjing university:natural sciences, 2015, 51(2):438-446.
[14] 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 measure of similarity between intuitionistic fuzzy rough sets[J]. Journal of computer applications, 2011, 31(5):1344-1347.
[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[J]. 计算机工程与应用, 2013, 49(9):140-143, 155. CHU Junfeng, WANG Yingming. Method of pattern recognition based on new similarity measure of interval-valued intu-itionistic fuzzy set[J]. Computer engineering and applications, 2013, 49(9):140-143, 155.
[16] 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. Intuitionistic fuzzy similarity measure approach based on orientation[J]. Systems engineering and electronics, 2015, 37(4):863-867.
[17] 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 software, 2008, 25(2):54-56.
[18] 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.
[19] NAMBURU A, SAMAYAMANTULA S K, EDARA S R. Generalised rough intuitionistic fuzzy c-means for magnetic resonance brain image segmentation[J]. IET image processing, 2017, 11(9):777-785.
[20] LIU Yong, LIN Yi. Intuitionistic fuzzy rough set model based on conflict distance and applications[J]. Applied soft computing, 2015, 31:266-273.
[21] 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.
[22] BORAN F E, AKAY D. A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition[J]. Information sciences, 2014, 255:45-57.
[23] 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 measures from fuzzy sets to intuitionistic fuzzy sets[J]. Journal of Xihua university:natural science, 2016, 35(2):17-24, 87.
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Last Update: 2018-08-25

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