基于粒计算的不确定性分析
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摘要
不确定性是一种普遍存在的现象。对于不确定性问题,来自哲学、认知科学、人工智能、粒计算等众多领域的研究者展开了不懈的探索。该文从粒计算的角度来认识不确定性,介绍了粒计算的主要理论模型,包括模糊集、粗糙集、商空间、三支决策、云模型,并从表示、度量、推理三方面概括了各模型的不确定性研究内容。在粗糙集理论背景下,重点从粒的表示、粒的度量、粒的关系、知识约简与规则提取等方面讨论分析了不确定性。
Uncertainty is the inability to specify something with precision,and it is a common phenomenon in the world. Many scholars have concentrated on the research of uncertainty from the fields of philosophy,cognitive science,artificial intelligence and granular computing. This paper analyses uncertainty from granular computing point of view,and examines some basic models of granular computing,including Fuzzy set,Rough set,Quotient space theory,Three-way decisions and cloud model. The presentations,measures and reasonings about uncertainty of these models have also been studied.
Uncertainty is the inability to specify something with precision,and it is a common phenomenon in the world. Many scholars have concentrated on the research of uncertainty from the fields of philosophy,cognitive science,artificial intelligence and granular computing. This paper analyses uncertainty from granular computing point of view,and examines some basic models of granular computing,including Fuzzy set,Rough set,Quotient space theory,Three-way decisions and cloud model. The presentations,measures and reasonings about uncertainty of these models have also been studied.
引文
[1]李德毅,杜鹢.不确定性人工智能[M].北京:国防工业出版社,2014.
[2]苗夺谦,张清华,钱宇华,等.从人类智能到机器实现模型———粒计算理论与方法[J].智能系统学报,2016,11(6):743-757.
[3] ZADEH L A. Fuzzy sets[J]. Information and Control,1965,8(3):338-353.
[4] ZADEH L A. Fuzzy logiccomputing with words[J].IEEE Transactions on Fuzzy Systems,1996,4(2):103-111.
[5] PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Sciences,1982,11(5):341-356.
[6]张铃,张钹.问题求解理论及应用[M].北京:清华大学出版社,1990.
[7] ZADEH L A. Fuzzy set and information granularity[C]∥Advance in Fuzzy Set Theory and Application,Amsterdam:North Holland,1979:3-18.
[8] HOBBS J R. Granularity[C]∥International Joint Conference on Artificial Intelligence, Los Angeles,USA,1985:432-435.
[9] LIN T Y. Granular computing on binary relations I:Data mining and neighborhood systems[J]. Rough Sets in Knowledge Discovery,1998(2):165-166.
[10] YAO Y Y. Granular Computing using Neighborhood Systems[M]∥Advances in Soft Computing. London:Springer,1999:539-553.
[11] LIU Q,JIANG F,DENG D. Design and Implement for diagnosis systems of hemorheology on blood viscosity syndrome based on Gr C[C]∥International Conference on Rough Sets,Fuzzy Sets,Data Mining,and Granular Computing. Springer-Verlag,2003:413-420.
[12]苗夺谦. Rough Set理论及其在机器学习中的应用研究[D].北京:中国科学院自动化研究所,1997.
[13]苗夺谦,王珏.粗糙集理论中知识粗糙性与信息熵关系的讨论[J].模式识别与人工智能,1998(1):34-40.
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[15]苗夺谦,范世栋.知识的粒度计算及其应用[J].系统工程理论与实践,2002,22(1):48-56.
[16]王国胤,张清华,马希骜等.知识不确定性问题的粒计算模型[J].软件学报,2011,22(4):000676-694.
[17]梁吉业,钱宇华.信息系统中的信息粒与熵理论[J].中国科学(技术科学),2008,38(12):2048-2065.
[18] 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.
[19]张燕平,张铃,赵姝,等.基于子模函数构建优化商空间链[J].南京大学学报(自然科学版),2016,52(6):1084-1089.
[20] 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.
[21] JING Y G,LI T R,HUANG J F,et al. An incremental attribute reduction approach based on knowledge granularity under the attribute generalization[J]. International Journal of Approximate Reasoning,2016,76:80-95.
[22] ZHANG X Y,MIAO D Q. Two basic double-quantitative Rough set models of precision and grade and their investigation using granular computing[J]. International Journal of Approximate Reasoning,2013,54(8):1130-1148.
[23] DUBOIS D,PRADE H. Rough Fuzzy sets and Fuzzy Rough sets[J]. International Journal of General Systems,1990,17(2-3):191-209.
[24] FENG Q,MIAO D,CHENG Y. Hierarchical decision rules mining[J]. Expert Systems with Applications,2010,37(3):2081-2091.
[25] WU W Z,LEUNG Y. Theory and applications of granular labelled partitions in multi-scale decision tables[J]. Information Sciences,2011,181(18):3878-3897.
[26]张铃,张钹.模糊商空间理论(模糊粒度计算方法)[J].软件学报,2003,14(4):770-776.
[27]张铃,张钹.模糊相容商空间与模糊子集[J].中国科学(信息科学),2011,41(1):1-11.
[28] YAO Y Y. Three-way decisions with probabilistic Rough sets[J]. Information Sciences,2010,180(3):341-353.
[29] HU Q B. Three-way decisions space and Three-way decisions[J]. Information Sciences,2014,281:21-52.
[30] LANG G,MIAO D,CAI M. Three-way decision approaches to conflict analysis using decision-theoretic Rough set theory[J]. Information Sciences,2017,406-407:185-207.
[31] XU J,MIAO D,ZHANG Y,et al. A Three-way decisions model with probabilistic Rough sets for stream computing[J]. International Journal of Approximate Reasoning,2017,88:1-22.
[32] ZHANG X,MIAO D. Three-way attribute reducts[J].International Journal of Approximate Reasoning,2017,88:401-434.
[33] ZHANG Y,ZHANG Z,MIAO D,et al. Three-way enhanced convolutional neural networks for sentencelevel sentiment classification[J]. Information Sciences,2019,477:55-64.
[34] PAWLAK Z. Rough Sets:Theoretical Aspects of Reasoning About Data[M]. Boston:Kluwer Academic Publishers,1991.
[35] BEAUBOUEF T,PETRY F E,ARORA G. Information-theoretic measures of uncertainty for rough sets and Rough relational databases[J]. Information Sciences,1998,109(14):185-195.
[36] LIANG J,SHI Z. The information entropy,Rough entropy and knowledge granulation in Rough set theory[J].International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,2004,12(01):37-46.
[37] QIAN J,LV P,YUE X,et al. Hierarchical attribute reduction algorithms for big data using MapReduce[J].Knowledge-Based Systems,2015,73(1):18-31.
[38] ZHANG X,MIAO D. Double-quantitative fusion of accuracy and importance:Systematic measure mining,benign integration construction,hierarchical attribute reduction[J]. Knowledge-Based Systems,2016,91:219-240.
[39] LIU C,MIAO D,QIAN J. On multi-granulation covering Rough sets[J]. International Journal of Approximate Reasoning,2014,55(6):1404-1418.
[40] LIU C H,MIAO D Q. On covering multi-granulation fuzzy Rough sets[J]. Information Technology Journal,2013,12(3):506-509.
[41]冯琴荣,苗夺谦,程昳.知识的划分粒度表示法[J].模式识别与人工智能,2009,22(1):65-69.
[42]刘财辉,苗夺谦,岳晓冬,等.知识不确定性度量及其关系研究[J].计算机科学,2014,41(3):66-70.
[43]苗夺谦,李道国.粗糙集理论、算法与应用[M].北京:清华大学出版社,2008.
[44] MIAO D,GAO C,ZHANG N,et al. Diverse reduct subspaces based co-training for partially labeled data[J]. International Journal of Approximate Reasoning,2011,52(8):1103-1117.
[45] PAWLAK Z. Some Issues on Rough Sets[M]∥Transactions on Rough Sets I. Berlin Heidelberg:Springer,2004:1-58.
[2]苗夺谦,张清华,钱宇华,等.从人类智能到机器实现模型———粒计算理论与方法[J].智能系统学报,2016,11(6):743-757.
[3] ZADEH L A. Fuzzy sets[J]. Information and Control,1965,8(3):338-353.
[4] ZADEH L A. Fuzzy logiccomputing with words[J].IEEE Transactions on Fuzzy Systems,1996,4(2):103-111.
[5] PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Sciences,1982,11(5):341-356.
[6]张铃,张钹.问题求解理论及应用[M].北京:清华大学出版社,1990.
[7] ZADEH L A. Fuzzy set and information granularity[C]∥Advance in Fuzzy Set Theory and Application,Amsterdam:North Holland,1979:3-18.
[8] HOBBS J R. Granularity[C]∥International Joint Conference on Artificial Intelligence, Los Angeles,USA,1985:432-435.
[9] LIN T Y. Granular computing on binary relations I:Data mining and neighborhood systems[J]. Rough Sets in Knowledge Discovery,1998(2):165-166.
[10] YAO Y Y. Granular Computing using Neighborhood Systems[M]∥Advances in Soft Computing. London:Springer,1999:539-553.
[11] LIU Q,JIANG F,DENG D. Design and Implement for diagnosis systems of hemorheology on blood viscosity syndrome based on Gr C[C]∥International Conference on Rough Sets,Fuzzy Sets,Data Mining,and Granular Computing. Springer-Verlag,2003:413-420.
[12]苗夺谦. Rough Set理论及其在机器学习中的应用研究[D].北京:中国科学院自动化研究所,1997.
[13]苗夺谦,王珏.粗糙集理论中知识粗糙性与信息熵关系的讨论[J].模式识别与人工智能,1998(1):34-40.
[14]苗夺谦,王珏.粗糙集理论中概念与运算的信息表示[J].软件学报,1999,10(2):113-116.
[15]苗夺谦,范世栋.知识的粒度计算及其应用[J].系统工程理论与实践,2002,22(1):48-56.
[16]王国胤,张清华,马希骜等.知识不确定性问题的粒计算模型[J].软件学报,2011,22(4):000676-694.
[17]梁吉业,钱宇华.信息系统中的信息粒与熵理论[J].中国科学(技术科学),2008,38(12):2048-2065.
[18] 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.
[19]张燕平,张铃,赵姝,等.基于子模函数构建优化商空间链[J].南京大学学报(自然科学版),2016,52(6):1084-1089.
[20] 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.
[21] JING Y G,LI T R,HUANG J F,et al. An incremental attribute reduction approach based on knowledge granularity under the attribute generalization[J]. International Journal of Approximate Reasoning,2016,76:80-95.
[22] ZHANG X Y,MIAO D Q. Two basic double-quantitative Rough set models of precision and grade and their investigation using granular computing[J]. International Journal of Approximate Reasoning,2013,54(8):1130-1148.
[23] DUBOIS D,PRADE H. Rough Fuzzy sets and Fuzzy Rough sets[J]. International Journal of General Systems,1990,17(2-3):191-209.
[24] FENG Q,MIAO D,CHENG Y. Hierarchical decision rules mining[J]. Expert Systems with Applications,2010,37(3):2081-2091.
[25] WU W Z,LEUNG Y. Theory and applications of granular labelled partitions in multi-scale decision tables[J]. Information Sciences,2011,181(18):3878-3897.
[26]张铃,张钹.模糊商空间理论(模糊粒度计算方法)[J].软件学报,2003,14(4):770-776.
[27]张铃,张钹.模糊相容商空间与模糊子集[J].中国科学(信息科学),2011,41(1):1-11.
[28] YAO Y Y. Three-way decisions with probabilistic Rough sets[J]. Information Sciences,2010,180(3):341-353.
[29] HU Q B. Three-way decisions space and Three-way decisions[J]. Information Sciences,2014,281:21-52.
[30] LANG G,MIAO D,CAI M. Three-way decision approaches to conflict analysis using decision-theoretic Rough set theory[J]. Information Sciences,2017,406-407:185-207.
[31] XU J,MIAO D,ZHANG Y,et al. A Three-way decisions model with probabilistic Rough sets for stream computing[J]. International Journal of Approximate Reasoning,2017,88:1-22.
[32] ZHANG X,MIAO D. Three-way attribute reducts[J].International Journal of Approximate Reasoning,2017,88:401-434.
[33] ZHANG Y,ZHANG Z,MIAO D,et al. Three-way enhanced convolutional neural networks for sentencelevel sentiment classification[J]. Information Sciences,2019,477:55-64.
[34] PAWLAK Z. Rough Sets:Theoretical Aspects of Reasoning About Data[M]. Boston:Kluwer Academic Publishers,1991.
[35] BEAUBOUEF T,PETRY F E,ARORA G. Information-theoretic measures of uncertainty for rough sets and Rough relational databases[J]. Information Sciences,1998,109(14):185-195.
[36] LIANG J,SHI Z. The information entropy,Rough entropy and knowledge granulation in Rough set theory[J].International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,2004,12(01):37-46.
[37] QIAN J,LV P,YUE X,et al. Hierarchical attribute reduction algorithms for big data using MapReduce[J].Knowledge-Based Systems,2015,73(1):18-31.
[38] ZHANG X,MIAO D. Double-quantitative fusion of accuracy and importance:Systematic measure mining,benign integration construction,hierarchical attribute reduction[J]. Knowledge-Based Systems,2016,91:219-240.
[39] LIU C,MIAO D,QIAN J. On multi-granulation covering Rough sets[J]. International Journal of Approximate Reasoning,2014,55(6):1404-1418.
[40] LIU C H,MIAO D Q. On covering multi-granulation fuzzy Rough sets[J]. Information Technology Journal,2013,12(3):506-509.
[41]冯琴荣,苗夺谦,程昳.知识的划分粒度表示法[J].模式识别与人工智能,2009,22(1):65-69.
[42]刘财辉,苗夺谦,岳晓冬,等.知识不确定性度量及其关系研究[J].计算机科学,2014,41(3):66-70.
[43]苗夺谦,李道国.粗糙集理论、算法与应用[M].北京:清华大学出版社,2008.
[44] MIAO D,GAO C,ZHANG N,et al. Diverse reduct subspaces based co-training for partially labeled data[J]. International Journal of Approximate Reasoning,2011,52(8):1103-1117.
[45] PAWLAK Z. Some Issues on Rough Sets[M]∥Transactions on Rough Sets I. Berlin Heidelberg:Springer,2004:1-58.