多粒度粗糙集的双层绝对约简
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摘要
多粒度粗糙集本质上是异构的,但是目前尚未运用于异构数据处理.从绝对约简的角度出发,提出多粒度粗糙集的双层绝对约简——多粒度绝对约简和多粒度绝对粒度约简.分析多粒度双层绝对约简的性质,特别是从异构数据约简的角度探究多粒度双层绝对约简的特性,提出多粒度双层绝对约简算法.理论分析和实例表明多粒度双层绝对约简算法的可行性.
Multi-granulation rough set is a rough set model for heterogenous data in essence. However,it is still not employed to deal with heterogenous data. From the viewpoints of absolute attribute reduction,double-level absolute reduction for multi-granulation rough sets is proposed,including multi-granulation absolute recducts and multi-granulation absolute granulation reducts, and properties of double-level absolute reduction are analyzed from the perspective of heterogenous data. The algorithms for double-level absolute reduction are presented. Theoretical analysis and example show the validation of multi-granulation absolute reducts, multi-granulation absolute granulation reducts and double-level absolute reducts.
Multi-granulation rough set is a rough set model for heterogenous data in essence. However,it is still not employed to deal with heterogenous data. From the viewpoints of absolute attribute reduction,double-level absolute reduction for multi-granulation rough sets is proposed,including multi-granulation absolute recducts and multi-granulation absolute granulation reducts, and properties of double-level absolute reduction are analyzed from the perspective of heterogenous data. The algorithms for double-level absolute reduction are presented. Theoretical analysis and example show the validation of multi-granulation absolute reducts, multi-granulation absolute granulation reducts and double-level absolute reducts.
引文
[1]PAWLAK Z.Rough Sets.International Journal of Computer and Information Sciences,1982,11(5):341-356.
[2]PAWLAK Z,SKOWRON A.Rudiments of Rough Sets.Information Sciences,2007,177(1):3-27.
[3]ZIAKO W.Variable Precision Rough Sets Model.Journal of Computer and System Sciences,1993,46(1):39-59.
[4]冯林,李天瑞,余志强.连续值属性决策表中的可变精度粗糙集模型及属性约简.计算机科学,2010,37(9):205-208.(FENG L,LI T R,YU Z Q.Attributes Reduction Based on the Variable Precision Rough Set in Decision Tables Containing Continuous-Valued Attributes.Computer Science,2010,37(9):205-208.)
[5]ZHU W,WANG F Y.Reduction and Axiomization of Covering Generalized Rough Sets.Information Sciences,2003,152:217-230.
[6]张灵均,徐久成,李双群,等.相斥邻域的覆盖粗糙集实值属性约简.山东大学学报(理学版),2012,47(1):77-82.(ZHANG L J,XU J C,LI S Q,et al.Numerical Attribute Reduction of Mutex Neighborhood Covering Rough Set Theory.Journal of Shandong University(Natural Science),2012,47(1):77-82.)
[7]YAO Y Y,WONG S K M.A Decision Theoretic Framework for Approximating Concepts.International Journal of Man-Machine Studies,1992,37(6):793-809.
[8]刘盾,姚一豫,李天瑞.三枝决策粗糙集.计算机科学,2011,38(1):246-250.(LIU D,YAO Y Y,LI T R.Three-Way Decision-Theoretic Rough Sets.Computer Science,2011,38(1):246-250.)
[9]DUBOIS D,PRADE H.Rough Fuzzy Sets and Fuzzy Rough Sets.International Journal of General Systems,1990,17(2/3):191-209.
[10]徐菲菲,苗夺谦,魏莱,等.基于互信息的模糊粗糙集属性约简.电子与信息学报,2008,30(6):1372-1375.(XU F F,MIAO D Q,WEI L,et al.Mutual Information-Based Algorithm for Fuzzy-Rough Attribute Reduction.Journal of Electronics&Information Technology,2008,30(6):1372-1375.)
[11]LIN T Y.Neighborhood Systems:A Qualitative Theory for Fuzzy and Rough Sets[M/OL].[2016-06-25].http://xanadu.cs.sjsu.edu/~tylin/publications/paper List/94.pdf.
[12]HU Q H,ZHANG L,ZHANG D,et al.Measuring Relevance between Discrete and Continuous Features Based on Neighborhood Mutual Information.Expert Systems with Applications:An International Journal,2011,38(9):10737-10750.
[13]SHI K Q,ZHAO J L.Function S-Rough Sets and Security-Authentication of Hiding Law.Science in China(Information Science),2008,51(7):924-935.
[14]SHI K Q,YAO B X.Function S-Rough Sets and Law Identification.Science in China(Information Science),2008,51(5):499-510.
[15]QIAN Y H,LIANG J Y,YAO Y Y,et al.MGRS:A Multi-granulation Rough Set.Information Sciences,2010,180(6):949-970.
[16]张明,唐振民,徐维艳,等.可变多粒度粗糙集模型.模式识别与人工智能,2012,25(4):709-720.(ZHANG M,TANG Z M,XU W Y,et al.Variable Multigranulation Rough Set Model.Pattern Recognition and Artificial Intelligence,2012,25(4):709-720.)
[17]邓大勇,陈林.并行约简与F-粗糙集//苗夺谦,王国胤,姚一豫,等,编.云模型与粒计算.北京:科学出版社,2012:210-228.(DENG D Y,CHEN L.Parallel Reducts and F-Rough Sets//MIAO D Q,WANG G Y,YAO Y Y,et al.,eds.Cloud Model and Granular Computing.Beijing,China:Science Press,2012:210-228.)
[18]陈林.粗糙集中不同粒度层次下的并行约简及决策.硕士学位论文.金华:浙江师范大学,2013.(CHEN L.Parallel Reducts and Decision in Various Levels of Granularity.Master Dissertation.Jinhua,China:Zhejiang Normal University,2013.)
[19]邓大勇,裴明华,黄厚宽.F-粗糙集方法对概念漂移的度量.浙江师范大学学报(自然科学版),2013,36(3):303-308.(DENG D Y,PEI M H,HUANG H K.The F-Rough Sets Approaches to the Measures of Concept Drift.Journal of Zhejiang Normal University(Natural Sciences),2013,36(3):303-308.)
[20]邓大勇,徐小玉,黄厚宽.基于并行约简的概念漂移探测.计算机研究与发展,2015,52(5):1071-1079.(DENG D Y,XU X Y,HUANG H K.Concept Drifting Detection for Categorical Evolving Data Based on Parallel Reducts.Journal of Computer Research and Development,2015,52(5):1071-1079.)
[21]顾力平,杨习贝.基于一般二元关系的多粒度粗糙集模型.南京航空航天大学学报,2013,45(1):124-129.(GU L P,YANG X B.Multigranulation Rough Set Models Based on General Binary Relations.Journal of Nanjing University of Aeronautics&Astronautics,2013,45(1):124-129.)
[22]李聪.多粒度模糊粗糙集研究.数学杂志,2016,36(1):124-134.(LI C.The Study on Multi-granulation Fuzzy Rough Set.Journal of Mathematics,2016,36(1):124-134.)
[23]桑妍丽,钱宇华.一种悲观多粒度粗糙集中的粒度约简算法.模式识别与人工智能,2012,25(3):361-366.(SAN Y L,QIAN Y H.A Granular Space Reduction Approach to Pessimistic Multi-granulation Rough Sets.Pattern Recognition and Artificial Intelligence,2012,25(3):361-366.)
[24]桑林,李续武.基于可变相容粒空间的多粒度覆盖粗糙集模型.计算机技术与发展,2015,25(8):35-38.(SANG L,LI X W.Multi-granule Covering Rough Sets Model Based on Variable Precision Tolerant-Granule Space.Computer Technology and Development,2015,25(8):35-38.)
[25]安虹.区间值信息系统多粒度粗糙集拓展模型的知识约简.硕士学位论文.临汾:山西师范大学,2014.(AN H.Knowledge Reduction Based on Multigranulation Rough Set Extended Model in Interval Valued Information System.Master Dissertation.Linfen,China:Shanxi Normal University,2014.)
[2]PAWLAK Z,SKOWRON A.Rudiments of Rough Sets.Information Sciences,2007,177(1):3-27.
[3]ZIAKO W.Variable Precision Rough Sets Model.Journal of Computer and System Sciences,1993,46(1):39-59.
[4]冯林,李天瑞,余志强.连续值属性决策表中的可变精度粗糙集模型及属性约简.计算机科学,2010,37(9):205-208.(FENG L,LI T R,YU Z Q.Attributes Reduction Based on the Variable Precision Rough Set in Decision Tables Containing Continuous-Valued Attributes.Computer Science,2010,37(9):205-208.)
[5]ZHU W,WANG F Y.Reduction and Axiomization of Covering Generalized Rough Sets.Information Sciences,2003,152:217-230.
[6]张灵均,徐久成,李双群,等.相斥邻域的覆盖粗糙集实值属性约简.山东大学学报(理学版),2012,47(1):77-82.(ZHANG L J,XU J C,LI S Q,et al.Numerical Attribute Reduction of Mutex Neighborhood Covering Rough Set Theory.Journal of Shandong University(Natural Science),2012,47(1):77-82.)
[7]YAO Y Y,WONG S K M.A Decision Theoretic Framework for Approximating Concepts.International Journal of Man-Machine Studies,1992,37(6):793-809.
[8]刘盾,姚一豫,李天瑞.三枝决策粗糙集.计算机科学,2011,38(1):246-250.(LIU D,YAO Y Y,LI T R.Three-Way Decision-Theoretic Rough Sets.Computer Science,2011,38(1):246-250.)
[9]DUBOIS D,PRADE H.Rough Fuzzy Sets and Fuzzy Rough Sets.International Journal of General Systems,1990,17(2/3):191-209.
[10]徐菲菲,苗夺谦,魏莱,等.基于互信息的模糊粗糙集属性约简.电子与信息学报,2008,30(6):1372-1375.(XU F F,MIAO D Q,WEI L,et al.Mutual Information-Based Algorithm for Fuzzy-Rough Attribute Reduction.Journal of Electronics&Information Technology,2008,30(6):1372-1375.)
[11]LIN T Y.Neighborhood Systems:A Qualitative Theory for Fuzzy and Rough Sets[M/OL].[2016-06-25].http://xanadu.cs.sjsu.edu/~tylin/publications/paper List/94.pdf.
[12]HU Q H,ZHANG L,ZHANG D,et al.Measuring Relevance between Discrete and Continuous Features Based on Neighborhood Mutual Information.Expert Systems with Applications:An International Journal,2011,38(9):10737-10750.
[13]SHI K Q,ZHAO J L.Function S-Rough Sets and Security-Authentication of Hiding Law.Science in China(Information Science),2008,51(7):924-935.
[14]SHI K Q,YAO B X.Function S-Rough Sets and Law Identification.Science in China(Information Science),2008,51(5):499-510.
[15]QIAN Y H,LIANG J Y,YAO Y Y,et al.MGRS:A Multi-granulation Rough Set.Information Sciences,2010,180(6):949-970.
[16]张明,唐振民,徐维艳,等.可变多粒度粗糙集模型.模式识别与人工智能,2012,25(4):709-720.(ZHANG M,TANG Z M,XU W Y,et al.Variable Multigranulation Rough Set Model.Pattern Recognition and Artificial Intelligence,2012,25(4):709-720.)
[17]邓大勇,陈林.并行约简与F-粗糙集//苗夺谦,王国胤,姚一豫,等,编.云模型与粒计算.北京:科学出版社,2012:210-228.(DENG D Y,CHEN L.Parallel Reducts and F-Rough Sets//MIAO D Q,WANG G Y,YAO Y Y,et al.,eds.Cloud Model and Granular Computing.Beijing,China:Science Press,2012:210-228.)
[18]陈林.粗糙集中不同粒度层次下的并行约简及决策.硕士学位论文.金华:浙江师范大学,2013.(CHEN L.Parallel Reducts and Decision in Various Levels of Granularity.Master Dissertation.Jinhua,China:Zhejiang Normal University,2013.)
[19]邓大勇,裴明华,黄厚宽.F-粗糙集方法对概念漂移的度量.浙江师范大学学报(自然科学版),2013,36(3):303-308.(DENG D Y,PEI M H,HUANG H K.The F-Rough Sets Approaches to the Measures of Concept Drift.Journal of Zhejiang Normal University(Natural Sciences),2013,36(3):303-308.)
[20]邓大勇,徐小玉,黄厚宽.基于并行约简的概念漂移探测.计算机研究与发展,2015,52(5):1071-1079.(DENG D Y,XU X Y,HUANG H K.Concept Drifting Detection for Categorical Evolving Data Based on Parallel Reducts.Journal of Computer Research and Development,2015,52(5):1071-1079.)
[21]顾力平,杨习贝.基于一般二元关系的多粒度粗糙集模型.南京航空航天大学学报,2013,45(1):124-129.(GU L P,YANG X B.Multigranulation Rough Set Models Based on General Binary Relations.Journal of Nanjing University of Aeronautics&Astronautics,2013,45(1):124-129.)
[22]李聪.多粒度模糊粗糙集研究.数学杂志,2016,36(1):124-134.(LI C.The Study on Multi-granulation Fuzzy Rough Set.Journal of Mathematics,2016,36(1):124-134.)
[23]桑妍丽,钱宇华.一种悲观多粒度粗糙集中的粒度约简算法.模式识别与人工智能,2012,25(3):361-366.(SAN Y L,QIAN Y H.A Granular Space Reduction Approach to Pessimistic Multi-granulation Rough Sets.Pattern Recognition and Artificial Intelligence,2012,25(3):361-366.)
[24]桑林,李续武.基于可变相容粒空间的多粒度覆盖粗糙集模型.计算机技术与发展,2015,25(8):35-38.(SANG L,LI X W.Multi-granule Covering Rough Sets Model Based on Variable Precision Tolerant-Granule Space.Computer Technology and Development,2015,25(8):35-38.)
[25]安虹.区间值信息系统多粒度粗糙集拓展模型的知识约简.硕士学位论文.临汾:山西师范大学,2014.(AN H.Knowledge Reduction Based on Multigranulation Rough Set Extended Model in Interval Valued Information System.Master Dissertation.Linfen,China:Shanxi Normal University,2014.)
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