形式概念分析的多粒度标记理论
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摘要
通过正向尺度化和反向尺度化方法,研究信息系统与形式背景之间的相互转化关系,利用经典形式背景给出多粒度标记形式背景的定义,证明多粒度标记形式背景与多粒度标记信息系统在语义上等价。对于多粒度标记形式背景,不同粒度标记下的蕴涵规则之间可以相互推理。所得结论为今后进一步研究形式概念分析的多粒度标记方法提供了理论基础。
By using forward and backward scaling approaches,the transformation relationship between information systems and formal contexts was clarified,and the notion of a multi-scale formal context was formally defined. It was verified that multi-scale formal contexts and multi-scale information systems could semantically be equivalent to each other. As for a multi-scale formal context,implication rules obtained from different scales were induced by each other. The obtained results could provide a theoretical reference for the further research of multi-scale approaches in formal concept analysis.
By using forward and backward scaling approaches,the transformation relationship between information systems and formal contexts was clarified,and the notion of a multi-scale formal context was formally defined. It was verified that multi-scale formal contexts and multi-scale information systems could semantically be equivalent to each other. As for a multi-scale formal context,implication rules obtained from different scales were induced by each other. The obtained results could provide a theoretical reference for the further research of multi-scale approaches in formal concept analysis.
引文
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[2]PAWLAK Z. Rough sets[J]. International Journal of Computer and Information Sciences,1982,11(5):341-356.
[3]YAO Yiyu. Concept lattices in rough set theory[C]//Proceedings of 2004 Annual Meeting of the North American Fuzzy Infor-mation Processing Society. Washington:IEEE,2004:796-801.
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[9]CHEN Jinkun,LI Jinjin,LIN Yaojin,et al. Relations of reduction between covering generalized rough sets and concept lattices[J]. Information Sciences,2015,304:16-27.
[10]TAN Anhui,LI Jinjin,LIN Guoping. Connections between covering-based rough sets and concept lattices[J]. InternationalJournal of Approximation Reasoning,2015,56:43-58.
[11]WANG Xia,ZHANG Wenxiu. Relations of attribute reduction between object and property oriented concept lattice[J].Know ledge-Based Systems,2008,21(5):398-403.
[12]魏玲,祁建军,张文修.概念格与粗糙集的关系研究[J].计算机科学,2006,33(3):18-21.WEI Ling,QI Jianjun,ZHANG Wenxiu. Study on relationships betw een concept lattice and rough set[J]. Computer Science,2006,33(3):18-21.
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[16]徐伟华,李金海,魏玲,等.形式概念分析理论与应用[M].北京:科学出版社,2016.XU Weihua,LI Jinhai,WEI Ling,et al. Formal concept analysis:theory and application[M]. Beijing:Science Press,2016.
[17]ZADEH L A.Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic[J].Fuzzy Sets and Systems,1997,90(2):111-127.
[18]LIN T Y. Granular computing on binary relations I:data mining and neighborhood systems[C]//Rough Sets in KnowledgeDiscovery. Berlin:Spring,1998:107-121.
[19]YAO Yiyu. Information granulation and rough set approximation[J]. International Journal of Intelligent Systems,2001,16:87-104.
[20]PEDRYCZ W,SKOWRON A,KREINOVICH V. Handbook of granular computing[M]. New York:Wiley,2008.
[21]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.M IAO Duoqian,WANG Guoyin,LIU Qing,et al. Granular computing:past,present and fature[M]. Beijing:SciencePress,2007.
[22]苗夺谦,徐菲菲,姚一豫,等.粒计算的集合论描述[J].计算机学报,2012,35(2):2351-2363.M IAO Duoqian,XU Feifei,YAO Yiyu,et al. Set-theoretic formulation of granular computing[J]. Chinese Journal of Com-puters,2012,35(2):2351-2363.
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[25]徐计,王国胤,于洪.基于粒计算的大数据处理[J].计算机学报,2015,38(8):1497-1517.XU Ji,WANG Guoyin,YU Hong. Review of big data processing based on granular computing[J]. Chinese Journal of Com-puters,2015,38(8):1497-1517.
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[27]MA Jianmin,ZHANG Wenxiu,LEUNG Yee,et al. Granular computing and dual Galois connection[J]. Information Sci-ences,2007,177(23):5365-5377.
[28]WU Weizhi,LEUNG Yee,MI Jusheng. Granular computing and knowledge reduction in formal contexts[J]. IEEE Transac-tions on Know ledge and Data Engineering,2009,21(10):1461-1474.
[29]LI Jinhai,MEI Changlin,CHERUKURI A K,et al. On rule acquisition in decision formal contexts[J]. International Journalof M achine Learning and Cybernetics,2013,4(6):721-731.
[30]GUO Lankun,HUANG Fangping,LI Qingguo,et al. Power contexts and their concept lattices[J]. Discrete Mathematics,2011,311:2049-2063.
[31]WEI Ling,WAN Qing. Granular transformation and irreducible element judgment theory based on pictorial diagrams[J].IEEE Transactions on Cybernetics,2017,46(2):380-387.
[32]KANG Xiangping,MIAO Duoqian. A variable precision rough set model based on the granularity of tolerance relation[J].Know ledge-Based Systems,2016,102:103-115.
[33]马垣,曾子维,迟呈英,等.形式概念及其新进展[M].北京:科学出版社,2011.M A Yuan,ZENG Ziw ei,CHI Chengying,et al. Formal concept and its new progress[M]. Beijing:Science Press,2011.
[34]LI Jinhai,REN Yue,MEI Changlin,et al. A comparative study of multigranulation rough sets and concept lattices via rule ac-quisition[J]. Know ledge-Based Systems,2016,91:152-164.
[35]SHAO Mingwen,LEUNG Yee,WANG Xizhao,et al. Granular reducts of formal fuzzy contexts[J]. Knowledge-Based Sys-tems,2016,114:156-166.
[36]ZHANG Qinghua,XING Yuke. Formal concept analysis based on granular computing[J]. Journal of Computational Informa-tion Systems,2010,6(7):2287-2296.
[37]张文修,徐伟华.基于粒计算的认知模型[J].工程数学学报,2008,24(6):957-971.ZHANG Wenxiu,XU Weihua. Cognitive model based on granular computing[J]. Chinese Journal of Engineering M athemat-ics,2007,24(6):957-971.
[38]XU Weihua,PANG Jinzhong,LUO Shuqun. A novel cognitive system model and approach to transformation of informationgranules[J]. International Journal of Approximate Reasoning,2014,55(3):853-866.
[39]XU Weihua,LI Wentao. Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets[J]. IEEE Transactions on Cybernetics,2016,46(2):366-379.
[40]QIAN Yuhua,LIANG Jiye,YAO Yiyu,et al. MGRS:a multi-granulation rough set[J]. Information Sciences,2010,180:949-970.
[41]QIAN Yuhua,LI Shunyong,LIANG Jiye,et al. Pessimistic rough set based decisions:a multigranulation fusion strategy[J].Information Sciences,2014,264:196-210.
[42]WU Weizhi,LEUNG YEE. Theory and applications of granular labeled partitions in multi-scale decision tables[J]. Informa-tion Sciences,2011,181:3878-3897.
[43]WU Weizhi,QIAN Yuhua,LI Tongjun,et al. On rule acquisition in incomplete multi-scale decision tables[J]. InformationSciences,2017,378:282-302.
[44]SHE Yanhong,LI Jinhai,YANG Hailong. A local approach to rule induction in multi-scale decision tables[J]. Knowledge-Based Systems,2015,89:398-410.
[45]LI Feng,HU Baoqing. A new approach of optimal scale selection to multi-scale decision tables[J]. Information Sciences,2017,381:193-208.
[46]LI Feng,HU Baoqing,WANG Jun. Stepwise optimal scale selection for multi-scale decision tables via attribute significance[J]. Knowledge-Based Systems,2017,129:4-16.
[47]HAO Chen,LI Jinhai,FAN Min,et al. Optimal scale selection in dynamic multi-scale decision tables based on sequentialthree-w ay decisions[J]. Information Sciences,2017,415/416:213-232.
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