多标记序决策系统中基于局部最优粒度的规则获取
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摘要
多粒度是当前粒计算研究的一个重要方面.在实践中,人们往往选择比较合适的粒度层次来解决问题.作为信息系统的一种特殊情况,多粒度决策系统是经常使用数据表示形式.在这样的系统中,对象可以在属性的不同粒度层次上取不同的观测值.实际使用时,常常遇到在数据属性上需要比较大小,即属性带有序关系.序关系分析是多指标决策的重要内容,而粗糙集是一种处理序关系有效方法.围绕多标记序决策系统的知识获取问题来开展研究,首先,介绍了多标记序决策系统的概念;然后,在协调的多标记序决策系统中定义了最优粒度和局部最优粒度,并介绍了基于局部最优粒度的属性约简和规则获取方法;最后,在不协调的多标记序决策系统中引入了广义决策,定义了广义最优粒度和广义局部最优粒度,并给出了基于广义局部最优粒度的属性约简和规则获取方法.
Multi granularity is an important issue of granular computing.In practice,people tend to choose the appropriate level of granularity to solve problems.As a special case of information system,multi-granular decision system can usually be observed in real-life world.In such system,objects may take different values under the same attribute measured at different granularity levels.When used in practice,it is often encountered that the data attribute needs to be ordered,that is,the attribute has an ordered relationship.Ordered relationship analysis is a class of important issues in multi-criteria decision making.Rough set is an effective approach to handle ordered relationship.Due to the rampant existence of multi-granular ordered decision systems in real world,the purpose of this study is to select appropriate level of granularity and to discuss rule acquisition from multi-granular ordered decision systems.Aiming at rules acquisition in multi-label ordered decision systems,the concept of multi-label ordered decision systems is introduced firstly.Then,notions of the optimal granularity and the local optimal granularity in consistent multi-label ordered decision system are defined,and the approaches to attribute reduction and rule extraction based on the local op-timal granularities are explored.Finally,the generalized decisions are introduced to inconsistent multi-label ordered decision systems,the generalized optimal granularity and the generalized local optimal granularity are also defined,and the approaches to attribute reduction and rule extraction based on the generalized local optimal granularities are further investigated.
Multi granularity is an important issue of granular computing.In practice,people tend to choose the appropriate level of granularity to solve problems.As a special case of information system,multi-granular decision system can usually be observed in real-life world.In such system,objects may take different values under the same attribute measured at different granularity levels.When used in practice,it is often encountered that the data attribute needs to be ordered,that is,the attribute has an ordered relationship.Ordered relationship analysis is a class of important issues in multi-criteria decision making.Rough set is an effective approach to handle ordered relationship.Due to the rampant existence of multi-granular ordered decision systems in real world,the purpose of this study is to select appropriate level of granularity and to discuss rule acquisition from multi-granular ordered decision systems.Aiming at rules acquisition in multi-label ordered decision systems,the concept of multi-label ordered decision systems is introduced firstly.Then,notions of the optimal granularity and the local optimal granularity in consistent multi-label ordered decision system are defined,and the approaches to attribute reduction and rule extraction based on the local op-timal granularities are explored.Finally,the generalized decisions are introduced to inconsistent multi-label ordered decision systems,the generalized optimal granularity and the generalized local optimal granularity are also defined,and the approaches to attribute reduction and rule extraction based on the generalized local optimal granularities are further investigated.
引文
[1]Zadeh L A.Fuzzy sets and information granularity.In:Gupta M M,Ragade R K,Yager R R.Advances in Fuzzy Set Theory and Applications.Amsterdam:North-Holland,1979:3-18.
[2]Lin T Y.Granular computing:Structures,representations,applications and future directions.In:Wang G Y,Liu Q,Yao Y Y,et al.Rough Sets,Fuzzy sets,Data Mining,Granular Computing.Springer Berlin Heidelberg,2003:16-24.
[3]Yao Y Y.Granular computing:Basic issues and possible solutions.In:Proceedings of the 5th Joint Conference on Computing and Information.Durham,NC,USA:Duke University Press,2000:186-189.
[4]张铃,张钹.基于商空间的问题求解:粒度计算的理论基础.北京:清华大学出版社,2014,382.
[5]梁吉业,钱宇华,李德玉等.大数据挖掘的粒计算理论与方法.中国科学:信息科学,2015,45(11):1355-1369.(Liang J Y,Qian Y H,Li D Y,et al.Theory and method of granular computing for big data mining.Scientia Sinica(Informationis),2015,45(11):1355-1369.)
[6]Yao J T,Vasilakos A V,Pedrycz W.Granular computing:Perspectives and challenges.IEEE Transactions on Cybernetics,2013,43(6):1977-1989.
[7]刘清,邱桃荣,刘斓.基于非标准分析的粒计算研究.计算机学报,2015,38(8):1618-1627.(Liu Q,Qiu T R,Liu L.The research of granular computing based on nonstandard analysis.Chinese Journal of Computers,2015,38(8):1618-1627.)
[8]Li H X,Zhang L B,Huang B,et al.Sequential three-way decision and granulation for cost-sensitive face recognition.Knowledge-Based Systems,2016,91:241-251.
[9]徐计,王国胤,于洪.基于粒计算的大数据处理.计算机学报,2015,38(8):1497-1517.(Xu J,Wang G Y,Yu H.Review of big data processing based on granular computing.Chinese Journal of Computers,2015,38(8):1497-1517.)
[10]Pedrycz W,Song M L.A granulation of linguistic information in AHP decision-making problems.Information Fusion,2014,17:93-101.
[11]Hu Q H,Yu D,Xie Z X.Fuzzy probabilistic approximation spaces and their information measures.IEEE Transactions on Fuzzy Systems,2006,14(2):191-201.
[12]Yu J H,Chen M H,Xu W H.Dynamic computing rough approximations approach to time-evolving information granule interval-valued ordered information system.Applied Soft Computing,2017,60:18-29.
[13]Shao M W,Leung Y,Wu W Z.Rule acquisition and complexity reduction in formal decision contexts.International Journal of Approximate Reasoning,2014,55(1):259-274.
[14]张清华,薛玉斌,王国胤.粗糙集的最优近似集.软件学报,2016,27(2):295-308.(Zhang Q H,Xue Y B,Wang G Y.Optimal approximation sets of rough sets.Journal of Software,2016,27(2):295-308.)
[15]Ge X,Wang P,Yun Z Q.The rough membership functions on four types of covering-based rough sets and their applications.Information Sciences,2017,390:1-14.
[16]Pawlak Z.Rough sets.International Journal of Computer&Information Science,1982,11(5):341-356.
[17]张文修,米据生,吴伟志.不协调目标信息系统的知识约简.计算机学报,2003,26(1):12-18.(Zhang W X,Mi J S,Wu W Z.Knowledge reductions in inconsistent information systems.Chinese Journal of Computers,2003,26(1):12-18.)
[18]王国胤,于洪,杨大春.基于条件信息熵的决策表约简.计算机学报,2002,25(7):759-766.(Wang G Y,Yu H,Yang D C.Decision table reduction based on conditional information entropy.Chinese Journal of Computers,2002,25(7):759-766.)
[19]Mi J S,Wu W Z,Zhang W X.Approaches to knowledge reduction based on variable precision rough set model.Information Sciences,2004,159(3-4):255-272.
[20]苗夺谦,胡桂荣.知识约简的一种启发式算法.计算机研究与发展,1999,36(6):681-684.(Miao D Q,Hu G R.A heuristic algorithm for reduction of knowledge.Journal of Computer Research&Development,1999,36(6):681-684.)
[21]Skowron A,Rauszer C.The discernibility matrices and functions in information systems.In:Slowinski R.Intelligent Decision Support:Handbook of Applications and Advances of the Rough Sets Theory.Dordrecht:Kluwer Academic Publisher,1992,11:331-362.
[22]Qian Y H,Liang J Y,Yao Y Y,et al.MGRS:A multi-granulation rough set.Information Sciences,2010,180(6):949-970.
[23]Qian Y H,Cheng H H,Wang J T,et al.Grouping granular structures in human granulation intelligence.Information Sciences,2017,382-383:150-169.
[24]Wu W Z,Leung Y.Theory and applications of granular labelled partitions in multi-scale decision tables.Information Sciences,2011,181(18):3878-3897.
[25]Wu W Z,Leung Y.Optimal scale selection for multi-scale decision tables.International Journal of Approximate Reasoning,2013,54(8):1107-1129.
[26]吴伟志,陈颖,徐优红等.协调的不完备多粒度标记决策系统的最优粒度选择.模式识别与人工智能,2016,29(2):108-115.(Wu W Z,Chen Y,Xu Y H,et al.Optimal granularity selections in consistent incomplete multi-granular labeled decision systems.Pattern Recognition&Artificial Intelligence,2016,29(2):108-115.)
[27]顾沈明,万雅虹,吴伟志等.多粒度决策系统的局部最优粒度选择.南京大学学报(自然科学),2016,52(2):280-288.(Gu S M,Wan Y H,Wu Y Z,et al.Local optimal granularity selections in multi-granular decision systems.Journal of Nanjing University(Natural Sciences),2016,52(2):280-288.)
[28]Gu S M,Wu W Z.On knowledge acquisition in multi-scale decision systems.International Journal of Machine Learning and Cybernetics,2013,4(5):477-486.
[29]顾沈明,胡超,吴伟志等.多标记序信息系统的不确定性研究,南京大学学报(自然科学),2015,51(2):377-383.(Gu S M,Hu C,Wu W Z,et al.Uncertainty measures in multi-label ordered information systems.Journal of Nanjing University(Natural Sciences),2015,51(2):377-383.)
[30]Li F,Hu B Q.A new approach of optimal scale selection to multi-scale decision tables.Information Sciences,2017,381:193-208.
[31]Greco S,Matarazzo B,Slowingski R.Rough approximation of a preference relation by dominance relations.European Journal of Operational Research,1999,117(1):63-83.
[32]Greco S,Matarazzo B,Slowinski R.Rough sets theory for multicriteria decision analysis.European Journal of Operational Research,2001,129(1):1-47.
[33]Greco S,Matarazzo B,Slowinski R.Rough approximation by dominance relations.International Journal of Inteligent Systems,2002,17(2):153-171.
[34]Greco S,Inuiguchi M,Slowinski R.Fuzzy rough sets and multiple-premise gradual decision rules.International Journal of Approximate Reasoning,2006,41(2):179-211.
[35]Shao M W,Zhang W X.Dominance relation and rules in an incomplete ordered information system.International Journal of Intelligent Systems,2005,20(1):13-27.
[36]Pan W,She K,Wei P Y.Multi-granulation fuzzy preference relation rough set for ordinal decision system.Fuzzy Sets and Systems,2017,312:87-108.
[37]Cheng Y,Miao D Q.Rule extraction based on granulation order in interval-valued fuzzy information system.Expert Systems with Applications,2011,38:12249-12261.
[38]顾沈明,顾金燕,吴伟志等.不完备多粒度决策系统的局部最优粒度选择.计算机研究与发展,2017,54(7):1500-1509.(Gu S M,Gu J Y,Wu W Z,et al.Local optimal granularity selections in incomplete multi-granular decision systems.Journal of Computer Research&Development,2017,54(7):1500-1509.)
[39]Wu W Z.Attribute reduction based on evidence theory in incomplete decision systems.Information Sciences,2008,178(5):1355-1371.
[2]Lin T Y.Granular computing:Structures,representations,applications and future directions.In:Wang G Y,Liu Q,Yao Y Y,et al.Rough Sets,Fuzzy sets,Data Mining,Granular Computing.Springer Berlin Heidelberg,2003:16-24.
[3]Yao Y Y.Granular computing:Basic issues and possible solutions.In:Proceedings of the 5th Joint Conference on Computing and Information.Durham,NC,USA:Duke University Press,2000:186-189.
[4]张铃,张钹.基于商空间的问题求解:粒度计算的理论基础.北京:清华大学出版社,2014,382.
[5]梁吉业,钱宇华,李德玉等.大数据挖掘的粒计算理论与方法.中国科学:信息科学,2015,45(11):1355-1369.(Liang J Y,Qian Y H,Li D Y,et al.Theory and method of granular computing for big data mining.Scientia Sinica(Informationis),2015,45(11):1355-1369.)
[6]Yao J T,Vasilakos A V,Pedrycz W.Granular computing:Perspectives and challenges.IEEE Transactions on Cybernetics,2013,43(6):1977-1989.
[7]刘清,邱桃荣,刘斓.基于非标准分析的粒计算研究.计算机学报,2015,38(8):1618-1627.(Liu Q,Qiu T R,Liu L.The research of granular computing based on nonstandard analysis.Chinese Journal of Computers,2015,38(8):1618-1627.)
[8]Li H X,Zhang L B,Huang B,et al.Sequential three-way decision and granulation for cost-sensitive face recognition.Knowledge-Based Systems,2016,91:241-251.
[9]徐计,王国胤,于洪.基于粒计算的大数据处理.计算机学报,2015,38(8):1497-1517.(Xu J,Wang G Y,Yu H.Review of big data processing based on granular computing.Chinese Journal of Computers,2015,38(8):1497-1517.)
[10]Pedrycz W,Song M L.A granulation of linguistic information in AHP decision-making problems.Information Fusion,2014,17:93-101.
[11]Hu Q H,Yu D,Xie Z X.Fuzzy probabilistic approximation spaces and their information measures.IEEE Transactions on Fuzzy Systems,2006,14(2):191-201.
[12]Yu J H,Chen M H,Xu W H.Dynamic computing rough approximations approach to time-evolving information granule interval-valued ordered information system.Applied Soft Computing,2017,60:18-29.
[13]Shao M W,Leung Y,Wu W Z.Rule acquisition and complexity reduction in formal decision contexts.International Journal of Approximate Reasoning,2014,55(1):259-274.
[14]张清华,薛玉斌,王国胤.粗糙集的最优近似集.软件学报,2016,27(2):295-308.(Zhang Q H,Xue Y B,Wang G Y.Optimal approximation sets of rough sets.Journal of Software,2016,27(2):295-308.)
[15]Ge X,Wang P,Yun Z Q.The rough membership functions on four types of covering-based rough sets and their applications.Information Sciences,2017,390:1-14.
[16]Pawlak Z.Rough sets.International Journal of Computer&Information Science,1982,11(5):341-356.
[17]张文修,米据生,吴伟志.不协调目标信息系统的知识约简.计算机学报,2003,26(1):12-18.(Zhang W X,Mi J S,Wu W Z.Knowledge reductions in inconsistent information systems.Chinese Journal of Computers,2003,26(1):12-18.)
[18]王国胤,于洪,杨大春.基于条件信息熵的决策表约简.计算机学报,2002,25(7):759-766.(Wang G Y,Yu H,Yang D C.Decision table reduction based on conditional information entropy.Chinese Journal of Computers,2002,25(7):759-766.)
[19]Mi J S,Wu W Z,Zhang W X.Approaches to knowledge reduction based on variable precision rough set model.Information Sciences,2004,159(3-4):255-272.
[20]苗夺谦,胡桂荣.知识约简的一种启发式算法.计算机研究与发展,1999,36(6):681-684.(Miao D Q,Hu G R.A heuristic algorithm for reduction of knowledge.Journal of Computer Research&Development,1999,36(6):681-684.)
[21]Skowron A,Rauszer C.The discernibility matrices and functions in information systems.In:Slowinski R.Intelligent Decision Support:Handbook of Applications and Advances of the Rough Sets Theory.Dordrecht:Kluwer Academic Publisher,1992,11:331-362.
[22]Qian Y H,Liang J Y,Yao Y Y,et al.MGRS:A multi-granulation rough set.Information Sciences,2010,180(6):949-970.
[23]Qian Y H,Cheng H H,Wang J T,et al.Grouping granular structures in human granulation intelligence.Information Sciences,2017,382-383:150-169.
[24]Wu W Z,Leung Y.Theory and applications of granular labelled partitions in multi-scale decision tables.Information Sciences,2011,181(18):3878-3897.
[25]Wu W Z,Leung Y.Optimal scale selection for multi-scale decision tables.International Journal of Approximate Reasoning,2013,54(8):1107-1129.
[26]吴伟志,陈颖,徐优红等.协调的不完备多粒度标记决策系统的最优粒度选择.模式识别与人工智能,2016,29(2):108-115.(Wu W Z,Chen Y,Xu Y H,et al.Optimal granularity selections in consistent incomplete multi-granular labeled decision systems.Pattern Recognition&Artificial Intelligence,2016,29(2):108-115.)
[27]顾沈明,万雅虹,吴伟志等.多粒度决策系统的局部最优粒度选择.南京大学学报(自然科学),2016,52(2):280-288.(Gu S M,Wan Y H,Wu Y Z,et al.Local optimal granularity selections in multi-granular decision systems.Journal of Nanjing University(Natural Sciences),2016,52(2):280-288.)
[28]Gu S M,Wu W Z.On knowledge acquisition in multi-scale decision systems.International Journal of Machine Learning and Cybernetics,2013,4(5):477-486.
[29]顾沈明,胡超,吴伟志等.多标记序信息系统的不确定性研究,南京大学学报(自然科学),2015,51(2):377-383.(Gu S M,Hu C,Wu W Z,et al.Uncertainty measures in multi-label ordered information systems.Journal of Nanjing University(Natural Sciences),2015,51(2):377-383.)
[30]Li F,Hu B Q.A new approach of optimal scale selection to multi-scale decision tables.Information Sciences,2017,381:193-208.
[31]Greco S,Matarazzo B,Slowingski R.Rough approximation of a preference relation by dominance relations.European Journal of Operational Research,1999,117(1):63-83.
[32]Greco S,Matarazzo B,Slowinski R.Rough sets theory for multicriteria decision analysis.European Journal of Operational Research,2001,129(1):1-47.
[33]Greco S,Matarazzo B,Slowinski R.Rough approximation by dominance relations.International Journal of Inteligent Systems,2002,17(2):153-171.
[34]Greco S,Inuiguchi M,Slowinski R.Fuzzy rough sets and multiple-premise gradual decision rules.International Journal of Approximate Reasoning,2006,41(2):179-211.
[35]Shao M W,Zhang W X.Dominance relation and rules in an incomplete ordered information system.International Journal of Intelligent Systems,2005,20(1):13-27.
[36]Pan W,She K,Wei P Y.Multi-granulation fuzzy preference relation rough set for ordinal decision system.Fuzzy Sets and Systems,2017,312:87-108.
[37]Cheng Y,Miao D Q.Rule extraction based on granulation order in interval-valued fuzzy information system.Expert Systems with Applications,2011,38:12249-12261.
[38]顾沈明,顾金燕,吴伟志等.不完备多粒度决策系统的局部最优粒度选择.计算机研究与发展,2017,54(7):1500-1509.(Gu S M,Gu J Y,Wu W Z,et al.Local optimal granularity selections in incomplete multi-granular decision systems.Journal of Computer Research&Development,2017,54(7):1500-1509.)
[39]Wu W Z.Attribute reduction based on evidence theory in incomplete decision systems.Information Sciences,2008,178(5):1355-1371.