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第6期 苗夺谦,等:从人类智能到机器实现模型一粒计算理论与方法 .755· on binary relation and covering[]].Information sciences, [56]张清华,王国胤,胡军.多粒度知识获取与不确定性度 2009,179(3):210-225. 量[M.北京:科学出版社,2013. [44]LIU Caihui,MIAO Duoqian,QIAN Jin.On multi-granula- ZHANG Qinghua,WANG Guoyin,HU Jun.Knowledge tion covering rough sets[].International journal of ap- acquisition of multi-granular and uncertainty measurements proximate reasoning,2014,55(6):1404-1418. [M].Beijing:Science Press,.2013.(未找到本条文献英 [45]LIU Caihui,PEDRYCZ W.Covering-based multi-granula- 文信息,请核对) tion fuzzy rough sets[].Journal of intelligent fuzzy sys- [57]刘宝碇,彭锦.不确定理论教程[M].北京:清华大学 tems,2016,30(1):303-318. 出版社.2005 [46]FENG Qinrong,MIAO Duoqian,CHENG Yi.Hierarchical LIU Baoding,PENG Jin.Tutorial of uncertainty theory decision rules mining[J].Expert systems with applica- [M].Beijing:Tsinghua Press,2005. tions,2010,37(3):2081-2091. [58]苗夺谦,李德毅,姚一豫,等.不确定性与粒计算[M]· [47]QIAN Jin,LV Ping,YUE Xiaodong et al.Hierarchical at- 北京:科学出版社,2011. tribute reduction algorithms for big data using MapReduce MIAO Duoqian,LI Deyi,YAO Yiyu,et al.Uncertainty [J].Knowledge-based systems.2015,73:18-31. and granular computing M].Beijing:Science Press, [48]CHEN Hongmei,LI Tianrui,RUAN Da.Maintenance of 2011. approximations in incomplete ordered decision systems [59]苗夺谦,王珏.粗糙集理论中知识粗糙性与信息嫡关系 while attribute values coarsening or refining[J].Knowl- 的讨论[J1.模式识别与人工智能,1998.11(1):34 edge-based systems,2012,31:140-161. 40. [49]CHEN Hongmei,LI Tianrui,LUO Chuan,et al.A rough MIAO Duogian,WANG Jue.On the relationships between set-based method for updating decision rules on attribute information entropy and roughness of knowledge in rough values'coarsening and refining[J].IEEE transactions on set theory[J].Pattern recognition artificial intelligence, knowledge and data engineering,2014,26(12):2886- 1998,11(1):34-40. 2899. [60]DE LUCA A,TERMINI S.A definition of a nonprobabilis- [50]张贤勇.基于精度与程度逻辑组合的几类粗糙集模型 tic entropy in the setting of fuzzy sets theory[].Informa- 及其算法研究[D].成都:四川师范大学,2011, tion and control,1972,20(4):301-312. ZHANG Xianyong.Study on several rough set models and [61]张文修,吴伟志,梁吉业,等.粗糙集理论与方法[M] their algorithms based on logical combinations of precision 北京:科学出版社.2001. and grade D].Chengdu:Sichuan Normal University, ZHANG Wenxiu,WU Weizhi,LIANG Jiye,et al.Rough 2011. sets theory and method[M].Beijing:Science Press, [51]XU Weihua,GUO Yanting.Generalized multigranulation 2001. double-quantitative decision-theoretic rough set [J]. [62 LIANG Jiye,SHI Zhongzhi.The information entropy, Knowledge-based systems,2016,105:190-205. rough entropy and knowledge granulation in rough set the- [52]FANG Bowen,HU Baoqing.Probabilistic graded rough set ory[].International journal of uncertainty,fuzziness and and double relative quantitative decision-theoretic rough set knowledge-based systems,2004,12(1):37-46. [J.International journal of approximate reasoning,2016, [63]DEMPSTER A P.Upper and lower probabilities induced by 74:1-12. a multivalued mapping[J].The annals of mathematical [53]ZHANG Xianyong,MIAO Duoqian.Double-quantitative statistics,1967,38(2):325-339. fusion of accuracy and importance:systematic measure [64]SHAFER G.A mathematical theory of evidence[M].Prin- mining,benign integration construction,hierarchical at- ceton:Princeton University Press,1976. tribute reduction J].Knowledge-based systems,2016, [65]苗夺谦,范世栋.知识的粒度计算及其应用[J].系统 91:219-240. 工程理论与实践,2002,22(1):48-56. [54]李德毅,刘常昱,杜鹊,等.不确定性人工智能[J].软 MIAO Duoqian,FAN Shidong.The calculation of knowl- 件学报.2004.15(11):1583-1594. edge granulation and its application[].Systems engineer- LI Deyi,LIU Changyu,DU Yi,et al.Artificial intelli- ing-theory practice,2002,22(1):48-56. gence with uncertainty[J].Journal of software,2004,15 [66]苗夺谦,王国胤,刘清等.粒计算:过去、现在与展望 (11):1583-1594. [M].北京:科学出版社,2007. [55]王国胤,张清华.不同知识粒度下粗糙集的不确定性研 [67]QIAN Yuhua,LIANG Jiye.Combination entropy and com- 究[J].计算机学报,2008,31(9):1588-1598. bination granulation in rough set theory[].International WANG Guoyin,ZHANG Qinghua.Uncertainty of rough journal of uncertainty,fuzziness and knowledge-based sys- sets in different knowledge granularities[J].Chinese jour- tems,2008,16(2):179-193. nal of computers,2008,31(9):1588-1598. [67]QIAN Yuhua,LIANG Jiye.Combination entropy and com-on binary relation and covering[ J]. Information sciences, 2009, 179(3): 210-225. [44]LIU Caihui, MIAO Duoqian, QIAN Jin. On multi⁃granula⁃ tion covering rough sets [ J]. International journal of ap⁃ proximate reasoning, 2014, 55(6): 1404-1418. [45]LIU Caihui, PEDRYCZ W. Covering⁃based multi⁃granula⁃ tion fuzzy rough sets[J]. Journal of intelligent & fuzzy sys⁃ tems, 2016, 30(1): 303-318. [46]FENG Qinrong, MIAO Duoqian, CHENG Yi. Hierarchical decision rules mining [ J]. Expert systems with applica⁃ tions, 2010, 37(3): 2081-2091. [47]QIAN Jin, LV Ping, YUE Xiaodong et al. Hierarchical at⁃ tribute reduction algorithms for big data using MapReduce [J]. Knowledge⁃based systems. 2015, 73:18-31. [48]CHEN Hongmei, LI Tianrui, RUAN Da. Maintenance of approximations in incomplete ordered decision systems while attribute values coarsening or refining [ J]. Knowl⁃ edge⁃based systems, 2012, 31: 140-161. [49]CHEN Hongmei, LI Tianrui, LUO Chuan, et al. A rough set⁃based method for updating decision rules on attribute values' coarsening and refining[ J]. IEEE transactions on knowledge and data engineering, 2014, 26( 12): 2886 - 2899. [50]张贤勇. 基于精度与程度逻辑组合的几类粗糙集模型 及其算法研究[D]. 成都: 四川师范大学, 2011. ZHANG Xianyong. Study on several rough set models and their algorithms based on logical combinations of precision and grade [ D]. Chengdu: Sichuan Normal University, 2011. [51] XU Weihua, GUO Yanting. Generalized multigranulation double⁃quantitative decision⁃theoretic rough set [ J ]. Knowledge⁃based systems, 2016, 105: 190-205. [52]FANG Bowen, HU Baoqing. Probabilistic graded rough set and double relative quantitative decision⁃theoretic rough set [ J]. International journal of approximate reasoning, 2016, 74: 1-12. [53] ZHANG Xianyong, MIAO Duoqian. Double⁃quantitative fusion of accuracy and importance: systematic measure mining, benign integration construction, hierarchical at⁃ tribute reduction [ J]. Knowledge⁃based systems, 2016, 91: 219-240. [54]李德毅, 刘常昱, 杜鹢, 等. 不确定性人工智能[ J]. 软 件学报, 2004, 15(11): 1583-1594. LI Deyi, LIU Changyu, DU Yi, et al. Artificial intelli⁃ gence with uncertainty[ J]. Journal of software, 2004, 15 (11): 1583-1594. [55]王国胤, 张清华. 不同知识粒度下粗糙集的不确定性研 究[J]. 计算机学报, 2008, 31(9): 1588-1598. WANG Guoyin, ZHANG Qinghua. Uncertainty of rough sets in different knowledge granularities[ J]. Chinese jour⁃ nal of computers, 2008, 31(9): 1588-1598. [56]张清华, 王国胤, 胡军. 多粒度知识获取与不确定性度 量[M]. 北京: 科学出版社, 2013. ZHANG Qinghua, WANG Guoyin, HU Jun. Knowledge acquisition of multi⁃granular and uncertainty measurements [M]. Beijing: Science Press, 2013. (未找到本条文献英 文信息,请核对) [57]刘宝碇, 彭锦. 不确定理论教程[M]. 北京: 清华大学 出版社, 2005. LIU Baoding, PENG Jin. Tutorial of uncertainty theory [M]. Beijing: Tsinghua Press, 2005. [58]苗夺谦, 李德毅, 姚一豫, 等. 不确定性与粒计算[M]. 北京: 科学出版社, 2011. MIAO Duoqian, LI Deyi, YAO Yiyu, et al. Uncertainty and granular computing [ M ]. Beijing: Science Press, 2011. [59]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, 11(1): 34- 40. MIAO Duoqian, WANG Jue. On the relationships between information entropy and roughness of knowledge in rough set theory[J]. Pattern recognition & artificial intelligence, 1998, 11(1): 34-40. [60]DE LUCA A, TERMINI S. A definition of a nonprobabilis⁃ tic entropy in the setting of fuzzy sets theory[ J]. Informa⁃ tion and control, 1972, 20(4): 301-312. [61]张文修, 吴伟志, 梁吉业, 等. 粗糙集理论与方法[M]. 北京: 科学出版社, 2001. ZHANG Wenxiu, WU Weizhi, LIANG Jiye, et al. Rough sets theory and method [ M ]. Beijing: Science Press, 2001. [62 ] LIANG Jiye, SHI Zhongzhi. The information entropy, rough entropy and knowledge granulation in rough set the⁃ ory[J]. International journal of uncertainty, fuzziness and knowledge⁃based systems, 2004, 12(1): 37-46. [63]DEMPSTER A P. Upper and lower probabilities induced by a multivalued mapping [ J]. The annals of mathematical statistics, 1967, 38(2): 325-339. [64]SHAFER G. A mathematical theory of evidence[M]. Prin⁃ ceton: Princeton University Press, 1976. [65]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. MIAO Duoqian, FAN Shidong. The calculation of knowl⁃ edge granulation and its application[J]. Systems engineer⁃ ing⁃theory & practice, 2002, 22(1): 48-56. [66]苗夺谦, 王国胤, 刘清等. 粒计算: 过去、现在与展望 [M]. 北京: 科学出版社, 2007. [67]QIAN Yuhua, LIANG Jiye. Combination entropy and com⁃ bination granulation in rough set theory[ J]. International journal of uncertainty, fuzziness and knowledge⁃based sys⁃ tems, 2008, 16(2): 179-193. [67]QIAN Yuhua, LIANG Jiye. Combination entropy and com⁃ 第 6 期 苗夺谦,等: 从人类智能到机器实现模型———粒计算理论与方法 ·755·
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