多粒度粗糙集数据分析研究的回顾与展望
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摘要
粒计算是知识表示和数据挖掘的一个基本问题。粗糙集理论是知识获取的一个典型粒计算模型。在传统粗糙集数据分析中,信息系统中每一个对象在每一个属性上只能取唯一的值。在实际生活数据中,根据不同的粒度或者尺度,对象在同一属性上可以取不同粒度的值。该文介绍目前流行的三类基于粗糙集的多粒度数据处理模型,即多粒化粗糙集模型、多粒度邻域粗糙集模型、多尺度信息系统的粗糙集数据分析模型,回顾这三类多粒度粗糙集数据分析模型的研究进展及主要研究内容,并提出若干研究问题。
Granular computing( Gr C) is a basic issue in knowledge representation and data mining. Rough set theory is a typical Gr C model for knowledge acquisition. In traditional rough set data analysis,each object under each attribute in an information system can only take on one value. However,in many real-life data,objects are usually measured at different scales/granularities under the same attribute. In this paper,three types of multi-granular rough-set-data-analysis models,which are called multi-granulation rough set model,multi-granular neighborhood rough set model,and multi-scale information system based rough set data analysis model,with their research progress are reviewed. And some problems are proposed for further study.
Granular computing( Gr C) is a basic issue in knowledge representation and data mining. Rough set theory is a typical Gr C model for knowledge acquisition. In traditional rough set data analysis,each object under each attribute in an information system can only take on one value. However,in many real-life data,objects are usually measured at different scales/granularities under the same attribute. In this paper,three types of multi-granular rough-set-data-analysis models,which are called multi-granulation rough set model,multi-granular neighborhood rough set model,and multi-scale information system based rough set data analysis model,with their research progress are reviewed. And some problems are proposed for further study.
引文
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[5]张铃,张钹.基于商空间的问题求解:粒度计算的理论基础[M].北京:清华大学出版社,2014.
[6]梁吉业,钱宇华,李德玉,等.大数据挖掘的粒计算理论与方法[J].中国科学(信息科学),2015,45(11):1355-1369.
[7]CHEN C L P,ZHANG C Y.Data-intensive applications,challenges,techniques and technologies:A survey on Big Data[J].Information Sciences,2014,275:314-347.
[8]PAWLAK Z.Rough Sets:Theoretical Aspects of Reasoning about Data[M].Boston:Kluwer Academic Publishers,1991.
[9]GANTER B,WILLE R.Formal Concept Analysis:Mathematical Foundations[M].New York:SpringerVerlag,1999.
[10]LIN T Y,YAO Y Y,ZADEH L A.Data Mining,Rough Sets and Granular Computing[M].New York:Physica-Verlag,2002.
[11]PEDRYCZ W,SKOWRON A,KREINOVICH V.Handbook of Granular Computing[M].New York:Wiley,2008.
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[14]YAO J T,VASILAKOSA V,PEDRYCZ W.Granular computing:Perspectives and challenges[J].IEEE Transactions on Cybernetics,2013,43(6):1977-1989.
[15]徐伟华,米据生,吴伟志.基于包含度的粒计算方法与应用[M].北京:科学出版社,2015.
[16]李金海,吴伟志.形式概念分析的粒计算方法及其研究展望[J].山东大学学报(理学版),2017,52(7):1-12.
[17]WU W Z,LEUNG Y,MI J S.Granular computing and knowledge reduction in formal contexts[J].IEEE Transactions on Knowledge and Data Engineering,2009,21(10):1461-1474.
[18]QIAN Y H,LIANG J Y,YAO Y Y,et al.MGRS:A multi-granulation rough set[J].Information Sciences,2010,180(6):949-970.
[19]QIAN Y H,LIANG J Y,DANG C Y.Incomplete multi-granulation rough set[J].IEEE Transactions on Systems,Man and Cybernetics,2010,40(2):420-431.
[20]QIAN Y H,LI S Y,LIANG J Y,et al.Pessimistic rough set based decisions:A multigranulation fusion strategy[J].Information Sciences,2014,264:196-210.
[21]ZHU P F,HU Q H,ZUO W M,et al.Multi-granularity distance metric learning via neighborhood granule margin maximization[J].Information Sciences,2014,282:321-331.
[22]ZHU P F,HU Q H.Adaptive neighborhood granularity selection and combination based on margin distribution optimization[J].Information Sciences,2013,249:1-12.
[23]LIN G P,QIAN Y H,LI J J.NMGRS:Neighborhoodbased multigranulation rough sets[J].International Journal of Approximate Reasoning,2012,53(7):1080-1093.
[24]HU Q H,YU D R,ME Z.Neighborhood classifiers[J].Expert Systems with Applications,2008,34(2):866-876.
[25]WU W Z,LEUNG Y.Theory and applications of granular labeled partitions in multi-scale decision tables[J].Information Sciences,2011,181(18):3878-3897.
[26]XU W H,WANG Q R,ZHANG X T.Multi-granulation rough sets based on tolerance relations[J].Soft Computing,2013,17(7):1241-1252.
[27]SUN B Z,MA W M.Multigranulation rough set theory over two universes[J].Journal of Intelligent&Fuzzy Systems,2015,28(3):1251-1269.
[28]SUN B Z,MA W M,QIAN Y H.Multigranulation fuzzy rough set over two universes and its application to decision making[J].Knowledge-Based Systems,2017,123:61-74.
[29]LIN G P,LIANG J Y,QIAN Y H.Multigranulation rough sets:From partition to covering[J].Information Sciences,2013,241:101-118.
[30]LIU C H,MIAO D Q,QIAN J.On multi-granulation covering rough sets[J].International Journal of Approximate Reasoning,2014,55(6):1404-1418.
[31]LIU C H,PEDRYCZ W,WANG M Z.Coveringbased multigranulation decision-theoretic rough sets[J].Journal of Intelligent&Fuzzy Systems,2017,32(1):749-765.
[32]MA J M,YAO Y Y.Rough set approximations in multi-granulation fuzzy approximation spaces[J].Fundamenta Informaticae,2015,142(1-4):145-160.
[33]XU W H,WANG Q R,LUO S Q.Multi-granulation fuzzy rough sets[J].Journal of Intelligent&Fuzzy Systems,2014,26(3):1323-1340.
[34]KONG Q Z,WEI Z X.Further study of multi-granulation fuzzy rough sets[J].Journal of Intelligent&Fuzzy Systems,2017,32(3):2413-2424.
[35]FENG T,MI J S.Variable precision multigranulation decision-theoretic fuzzy rough sets[J].KnowledgeBased Systems,2016,91:93-101.
[36]HUANG B,GUO C X,ZHANG Y L,et al.Intuitionistic fuzzy multigranulation rough sets[J].Information Sciences,2014,277:299-320.
[37]ZHANG H D,HE Y P,XIONG L L.Multi-granulation dual hesitant fuzzy rough sets[J].Journal of Intelligent&Fuzzy Systems,2016,30(2):623-637.
[38]VAN T L,HU B Q.L-fuzzy multigranulation rough set based on residuated lattices[J].Journal of Intelligent&Fuzzy Systems,2016,30(5):2821-2831.
[39]ZHANG C,LI D Y,MU Y M.An interval-valued hesitant fuzzy multigranulation rough set over two universes model for steam turbine fault diagnosis[J].Applied Mathematical Modelling,2017,42:693-704.
[40]SHE Y H,HE X L,SHI H X.A multiple-valued logic approach for multigranulation rough set model[J].International Journal of Approximate Reasoning,2017,82:270-284.
[41]LI J H,HUANG C C,QI J J.Three-way cognitive concept learning via multi-granularity[J].Information Sciences,2017,378:244-263.
[42]LI J H,REN Y,MEI C L,et al.A comparative study of multigranulation rough sets and concept lattices via rule acquisition[J].Knowledge-Based Systems,2016,91:152-164.
[43]KANG X P,LI D Y,WANG S,et al.Formal concept analysis based on fuzzy granularity base for different granulations[J].Fuzzy Sets and Systems,2012,203:33-48.
[44]YANG X B,SONG X N,CHEN Z H.On multigranulation rough sets in incomplete information system[J].International Journal of Machine Learning and Cybernetics,2012,3(3):223-232.
[45]YANG H L,GUO Z L.Multigranulation decision-theoretic rough sets in incomplete information systems[J].International Journal of Machine Learning and Cybernetics,2015,6(6):1005-1018.
[46]PAN W,SHE K,WEI P Y.Multi-granulation fuzzy preference relation rough set for ordinal decision system[J].Fuzzy Sets and Systems,2017,312:87-108.
[47]JU H R,LI H X,YANG X B.Cost-sensitive rough set:A multi-granulation approach[J].KnowledgeBased Systems,2017,123:137-153.
[48]LIU X,QIAN Y H,LIANG J Y.A rule-extraction framework under multigranulation rough sets[J].International Journal of Machine Learning and Cybernetics,2014,5(2):319-326.
[49]YANG X B,QI Y,YU H L.Updating multigranulation rough approximations with increasing of granular structures[J].Knowledge-Based Systems,2014,64:59-69.
[50]ZHANG Q H,ZHANG Q,WANG G Y.The uncertainty of probabilistic rough sets in multi-granulation spaces[J].International Journal of Approximate Reasoning,2016,77:38-54.
[51]FEN T,FAN H T,MI J S.Uncertainty and reduction of variable precision multigranulation fuzzy rough sets based on three-way decisions[J].International Journal of Approximate Reasoning,2017,85:36-58.
[52]MA Z M,MI J S.A comparative study of MGRSs and their uncertainty measures[J].Fundamenta Informaticae,2015,142(1-4):161-181.
[53]LIN G P,LIANG J Y,QIAN Y H.Uncertainty measures for multigranulation approximation space[J].International Journal of Uncertainty Fuzziness and Knowledge-Based Systems,2015,23(3):443-457.
[54]TAN A H,WU W Z,TAO Y Z.On the belief structures and reductions of multigranulation spaces with decisions[J].International Journal of Approximate Reasoning,2017,88:39-52.
[55]TAN A H,WU W Z,LI J J,et al.Evidence-theorybased numerical characterization of multigranulation rough sets in incomplete information systems[J].Fuzzy Sets and Systems,2016,294:18-35.
[56]ZENG K,SHE K,NIU X Z.Multi-granulation entropy and its applications[J].Entropy,2013,15(6):2288-2302.
[57]HUNAG B,LI H X,FENG G F,et al.Inclusion measure-based multi-granulation intuitionistic fuzzy decision-theoretic rough sets and their application to ISSA[J].Knowledge-Based Systems,2017,138:220-231.
[58]LIN Y J,LI J J,LIN P R,et al.Feature selection via neighborhood multi-granulation fusion[J].Knowledge-Based Systems,2014,67:162-168.
[59]ZHAO H,ZHU W.Optimal cost-sensitive granularization based on rough sets for variable costs[J].Knowledge-Based Systems,2014,65:72-82.
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