[1]车晓雅,李磊军,米据生.基于证据理论刻画多粒度覆盖粗糙集的数值属性[J].智能系统学报,2016,11(4):481-486.[doi:10.11992/tis.201606011]
CHE Xiaoya,LI Leijun,MI Jusheng.Evidence-theory-based numerical characterization of multi-granulation covering rough sets[J].CAAI Transactions on Intelligent Systems,2016,11(4):481-486.[doi:10.11992/tis.201606011]
点击复制
CHE Xiaoya,LI Leijun,MI Jusheng.Evidence-theory-based numerical characterization of multi-granulation covering rough sets[J].CAAI Transactions on Intelligent Systems,2016,11(4):481-486.[doi:10.11992/tis.201606011]
基于证据理论刻画多粒度覆盖粗糙集的数值属性
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
11
期数:
2016年第4期
页码:
481-486
栏目:
学术论文—知识工程
出版日期:
2016-07-25
- Title:
- Evidence-theory-based numerical characterization of multi-granulation covering rough sets
- Keywords:
- rough sets theory; covering; granulation; evidence theory; approximation; characterization
- 分类号:
- TP18
- 摘要:
- 在经典多粒度粗糙集模型的基础上，基于论域中对象的极大描述和极小描述，定义了4种应用更为广泛的悲观多粒度覆盖粗糙集模型。然后通过集合的交、并运算与关系划分函数，构造了对象关于覆盖族的单粒度的多元覆盖及单粒度划分。在此基础上，基于证据理论，探讨了4种悲观多粒度覆盖粗糙集的上、下近似与信任函数和似然函数之间关系，并描述了该模型所具备的相关数值属性。对比分析表明悲观多粒度覆盖粗糙集模型既具备经典多粒度粗糙集模型能够融合多源信息的优势，又克服了其应用范围狭窄的缺点。实例分析验证了所提模型的有效性。
- Abstract:
- Considering classical multi-granulation rough sets and using the maximal and minimal descriptors of objects in a given universe, this paper proposes four pessimistic multi-granulation covering rough set models, suitable for extensive application. Based on set union and portion functions, the notion of multi-granularity covering connected to a number of coverings and a single granularity partition in the domain are defined. On this basis, belief and plausibility functions from evidence theory are employed to define the relationship between the upper and lower approximations, the belief function, and the likelihood function, and to characterize the set approximations in the four models. Compared with classical multi-granulation rough sets, the pessimistic multi-granulation covering rough set models not only have distinct advantages and combine multi-source information, but also avoid the shortcomings of a narrow application range. Finally, a real example is used to demonstrate the effectiveness of the presented models.
- 参考文献/References:
-
[1] PALAWK Z. Rough set[J]. International journal of computer & information sciences, 1982, 11(5):341-356.
[2] CHEN Degang, KWONG S, HE Qiang, et al. Geometrical interpretation and applications of membership functions with fuzzy rough sets[J]. Fuzzy sets and systems, 2012, 193:122-135.
[3] LIANG Jiye, CHIN K S, Dang Chuangyin, et al. A new method for measuring uncertainty and fuzziness in rough set theory[J]. International journal of general systems, 2002, 31(4):331-342.
[4] LIANG Jiye, WANG Feng, DANG Chaungyin, et al. A group incremental approach to feature selection applying rough set technique[J]. IEEE transactions on knowledge and data engineering, 2014, 26(2):294-308.
[5] TAN Anhui, LI Jinjin, LIN Guoping. Extended results on the relationship between information systems[J]. Information sciences, 2015, 290:156-173.
[6] BONIKOWSKI Z, BRYNIARSKI E, WYBRANIEC-SKARDOWSKA U. Extensions and intentions in the rough set theory[J]. Information sciences, 1998, 107(1/2/3/4):149-167.
[7] FENG Tao, MI Jusheng, WU Weizhi. Covering-based generalized rough fuzzy sets[M]//WANG Guoying, PETERS J F, SKOWRON A, et al. Rough Sets and Knowledge Technology. Berlin Heidelberg:Springer, 2006:208-215.
[8] QIAN Y H, LIANG J Y. Rough set method based on multi-granulations[C]//Proceedings of the 5th IEEE International Conference on Cognitive Informatics. Beijing:IEEE, 2006:297-304.
[9] 徐伟华, 刘士虎, 张文修. 一般二元关系下信息系统知识的粒度描述[J]. 计算机工程与应用, 2011, 47(18):40-44. XU Weihua, LIU Shihu, ZHANG Wenxiu. Granularity representation of knowledge in information system based on general binary-relation[J]. Computer engineering and applications, 2011, 47(18):40-44.
[10] QIAN Yuhua, LIANG Jiye, YAO Yiyu, et al. MGRS:a multi-granulation rough set[J]. Information sciences, 2010, 180(6):949-970.
[11] LIU Caihui, MIAO Duoqian, QIAN Jin. On multi-granulation covering rough sets[J]. International journal of approximate reasoning, 2014, 55(6):1404-1418.
[12] DEMPSTER A P. Upper and lower probability inferences based on a sample from a finite univariate population[J]. Biometrika, 1967, 54(3/4):515-528.
[13] SHAFER G. A mathematical theory of evidence[J]. Technometrics, 1978, 20(1):242.
[14] LIN Guoping, LIANG Jiye, QIAN Yuhua. An information fusion approach by combining multigranulation rough sets and evidence theory[J]. Information sciences, 2015, 314:184-199.
[15] 林国平. 覆盖广义粗糙集与信任函数[J]. 漳州师范学院学报:自然科学版, 2010(2):1-4. LIN Guoping. Connections between covering generization rough set and dempster-shafer theory of evidence[J]. Journal of Zhangzhou normal university:natural science, 2010(2):1-4.
[16] WU Weizhi, MI Jushneg. Knowledge reduction in incomplete information systems based on dempster-shafer theory of evidence[M]//WANG Guoying, PETERS J F, SKOWRON A, et al. Rough Sets and Knowledge Technology. Berlin Heidelberg:Springer, 2006:254-261.
[17] YAO Y Y, LINGRAS P J. Interpretations of belief functions in the theory of rough sets[J]. Information sciences, 1998, 104(1/2):81-106.
[18] CHEN Degang, ZHANG Xiaoxia, LI Wanlu. On measurements of covering rough sets based on granules and evidence theory[J]. Information sciences, 2015, 317:329-348.
[19] CHEN Degang, LI Wanlu, ZHANG Xiao, et al. Evidence-theory-based numerical algorithms of attribute reduction with neighborhood-covering rough sets[J]. International journal of approximate reasoning, 2014, 55(3):908-923.
[20] WU Weizhi, LEUNG Y, ZHANG Wenxiu. Connections between rough set theory and Dempster-Shafer theory of evidence[J]. International journal of general systems, 2002, 31(4):405-430.
[21] 吴伟志, 米据生, 李同军. 无限论域中的粗糙近似空间与信任结构[J]. 计算机研究与发展, 2012, 49(2):327-336. WU Weizhi, MI Jusheng, LI Tongjun. Rough approximation spaces and belief structures in infinite universes of discourse[J]. Journal of computer research and development, 2012, 49(2):327-336.
[22] TAN Anhui, WU Weizhi, LI Jinjin, et al. Evidence-theory-based numerical characterization of multi-granulation rough sets in incomplete information systems[J]. Fuzzy sets and systems, 2016, 294:18-35.
[23] ZAKOWSKI B W. Approximations in the space (u, π)[J]. Demonstratio mathematica, 1983, 16(3):761-769.
- 相似文献/References:
-
[1]余华平,郭梅.面向管道系统的无线传感器网络三维节点部署算法[J].智能系统学报,2013,8(4):333.[doi:10.3969/j.issn.1673-4785.201304025]
YU Huaping,GUO Mei.The research of three-dimensional node deployment of wireless sensor network for pipeline systems[J].CAAI Transactions on Intelligent Systems,2013,8():333.[doi:10.3969/j.issn.1673-4785.201304025]
[2]汤建国,汪江桦,韩莉英,等.基于覆盖粗糙集的语言动力系统[J].智能系统学报,2014,9(2):229.[doi:10.3969/j.issn.1673-4785.201307018]
TANG Jianguo,WANG Jianghua,HAN Liying,et al.Linguistic dynamic systems based on covering-based rough sets[J].CAAI Transactions on Intelligent Systems,2014,9():229.[doi:10.3969/j.issn.1673-4785.201307018]
[3]韦碧鹏,吕跃进,李金海.α优势关系下粗糙集模型的属性约简[J].智能系统学报,2014,9(2):251.[doi:10.3969/j.issn.1673-4785.201307012]
WEI Bipeng,Lü Yuejin,LI Jinhai.Attribute reduction based on the rough set model under α dominance relation[J].CAAI Transactions on Intelligent Systems,2014,9():251.[doi:10.3969/j.issn.1673-4785.201307012]
[4]刘财辉,蔡克参.元素最小描述并集下的多粒度覆盖粗糙集模型[J].智能系统学报,2016,11(4):534.[doi:10.11992/tis.201605034]
LIU Caihui,CAI Kecan.Multigranulation covering rough sets based on the union of minimal descriptions of elements[J].CAAI Transactions on Intelligent Systems,2016,11():534.[doi:10.11992/tis.201605034]
[5]王映龙,曾淇,钱文彬,等.变精度下不完备邻域决策系统的属性约简算法[J].智能系统学报,2017,12(3):386.[doi:10.11992/tis.201705027]
WANG Yinglong,ZENG Qi,QIAN Wenbin,et al.Attribute reduction algorithm of the incomplete neighborhood decision system with variable precision[J].CAAI Transactions on Intelligent Systems,2017,12():386.[doi:10.11992/tis.201705027]
[6]胡霞,费鹏,杜卫锋.集族等价与基于粒的下近似算子研究[J].智能系统学报,2018,13(2):327.[doi:10.11992/tis.201607018]
HU Xia,FEI Peng,DU Weifeng.On collections equivalence and the granule based lower approximation operators[J].CAAI Transactions on Intelligent Systems,2018,13():327.[doi:10.11992/tis.201607018]
[7]刘盾,李天瑞,梁德翠,等.三支决策的时空性[J].智能系统学报,2019,14(1):141.[doi:10.11992/tis.201804045]
LIU Dun,LI Tianrui,LIANG Decui,et al.Temporality and spatiality of three-way decisions[J].CAAI Transactions on Intelligent Systems,2019,14():141.[doi:10.11992/tis.201804045]
[8]刘盾,李天瑞,杨新,等.三支决策-基于粗糙集与粒计算研究视角[J].智能系统学报,2019,14(6):1111.[doi:10.11992/tis.201905039]
LIU Dun,LI Tianrui,YANG Xin,et al.Three-way decisions: research perspectives for rough sets and granular computing[J].CAAI Transactions on Intelligent Systems,2019,14():1111.[doi:10.11992/tis.201905039]
[9]何强,张娇阳.核对齐多核模糊支持向量机[J].智能系统学报,2019,14(6):1163.[doi:10.11992/tis.201904050]
HE Qiang,ZHANG Jiaoyang.Kernel-target alignment multi-kernel fuzzy support vector machine[J].CAAI Transactions on Intelligent Systems,2019,14():1163.[doi:10.11992/tis.201904050]
备注/Memo
收稿日期:2016-06-03。
基金项目:国家自然科学基金项目（61573127，61502144，61300121，6147 2463）；河北省自然科学基金项目（A2014205157）；河北省高校创新团队领军人才培育计划项目（LJRC022）；河北省高校自然科学基金项目（QN2016133）；河北师范大学博士科学基金项目（L2015B01）；河北省教育厅研究生创新项目（sj2015001）.
作者简介:车晓雅,女,1991年生,硕士研究生,主要研究方向为人工智能的数学基础;李磊军,男,1985年生,讲师,博士,主要研究方向为粗糙集,概念格,粒计算与集成学习等,已发表学术论文10余篇,其中被SCI检索5篇。
通讯作者:车晓雅.E-mail:chexiaoya@163.com.
更新日期/Last Update:
1900-01-01