JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (5): 1-12.doi: 10.6040/j.issn.1671-9352.c.2020.002

    Next Articles

Optimization of class-attribute block in multi-granularity formal concept analysis

LI Jin-hai1,2, HE Jian-jun1,2, WU Wei-zhi3,4   

  1. 1. Data Science Research Center, Kunming University of Science and Technology, Kunming 650500, Yunnan, China;
    2. Faculty of Science, Kunming University of Science and Technology, Kunming 650500, Yunnan, China;
    3. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022, Zhejiang, China;
    4. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan 316022, Zhejiang, China
  • Published:2020-05-06

PDF (PC)

1410

Abstract: The existing meso-granularity labeled method in the multi-granularity formal concept analysis is not able to realize the cross-granularity combination for the internal information of class-attribute blocks. Motivated by this problem, this paper divides the internal information of a class-attribute block into sub-classes based on the requirements of practical applications, and puts forward multi-granularity class-attribute blocks by means of combining the obtained sub-classes in a cross-granularity way. Then it analyzes the internal structure of multi-granularity class-attribute blocks, and reveals the mechanism of how to update decision implications when the multi-granularity class-attribute block becomes from coarse to fine or fine to coarse. The obtained results in this paper can further improve the theory and method of multi-level knowledge discovery with multi-granularity formal concept analysis.

Key words: granular computing, formal concept analysis, concept lattice, multi-granularity formal context, multi-granularity class-attribute block

CLC Number: 

  • TP18
[1] WILLE R. Restructuring lattice theory: an approach based on hierarchies of concepts[C] //Ordered Sets. Berlin: Springer, 1982: 445-470.
[2] 谢志鹏, 刘宗田. 概念格的快速渐进式构造算法[J]. 计算机学报, 2002, 25(5):490-496. XIE Zhipeng, LIU Zongtian. A fast incremental algorithm for building concept lattice[J]. Chinese Journal of Computers, 2002, 25(5):490-496.
[3] 张文修, 魏玲, 祁建军. 概念格的属性约简理论与方法[J]. 中国科学E辑: 信息科学, 2005, 35(6):628-639. ZHANG Wenxiu, WEI Ling, QI Jianjun. Attribute reduction theory and approach to concept lattice[J]. Science in China Series E: Information Sciences, 2005, 35(6):628-639.
[4] 李进金, 张燕兰, 吴伟志, 等. 形式背景与协调决策形式背景属性约简与概念格生成[J]. 计算机学报, 2014, 37(8):1168-1774. LI Jinjin, ZHANG Yanlan, WU Weizhi, et al. Attribute reduction for formal context and consistent decision formal context and concept lattice generation[J]. Chinese Journal of Computers, 2014, 37(8):1168-1774.
[5] SHAO Mingwen, LIU Min, ZHANG Wenxiu. Set approximations in fuzzy formal concept analysis[J]. Fuzzy Sets and Systems, 2007, 158(23):2627-2640.
[6] ZHANG Zhuo. Constructing L-fuzzy concept lattices without fuzzy Galois closure operation[J]. Fuzzy Sets and Systems, 2018, 333:71-86.
[7] 马垣, 张学东, 迟呈英. 紧致依赖与内涵亏值[J]. 软件学报, 2011, 22(5):962-971. MA Yuan, ZHANG Xuedong, CHI Chengying. Compact dependencies and intent waned values[J]. Journal of Software, 2011, 22(5):962-971.
[8] WANG Lidong, LIU Xiaodong. Concept analysis via rough set and AFS algebra[J]. Information Sciences, 2008, 178(21):4125-4137.
[9] CHEN Jinkun, MI Jusheng, XIE Bin, et al. A fast attribute reduction method for large formal decision contexts[J]. International Journal of Approximate Reasoning, 2019, 106:1-17.
[10] 王霞, 江山, 李俊余, 等. 三元概念的一种构造方法[J]. 计算机研究与发展, 2019, 56(4):844-853. WANG Xia, JIANG Shan, LI Junyu, et al. A construction method of triadic concepts[J]. Journal of Computer Research and Development, 2019, 56(4):844-853.
[11] 胡可云, 陆玉昌, 石纯一. 概念格及其应用进展[J]. 清华大学学报(自然科学版), 2000, 40(9):77-81. HU Keyun, LU Yuchang, SHI Chunyi. Advances in concept lattice and its application[J]. Journal of Tsinghua University(Science & Technology), 2000, 40(9):77-81.
[12] POELMANS J, IGNATOV D I, KUZNETSOV S O, et al. Fuzzy and rough formal concept analysis: a survey[J]. International Journal of General Systems, 2014, 43(2):105-134.
[13] 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.
[14] QI Jianjun, QIAN Ting, WEI Ling. The connections between three-way and classical concept lattices[J]. Knowledge-Based Systems, 2016, 91:143-151.
[15] LI Jinhai, HUANG Chenchen, QI Jianjun, et al. Three-way cognitive concept learning via multi-granularity[J]. Information Sciences, 2017, 378:244-263.
[16] ZHI Huilai, LI Jinhai. Granule description based on formal concept analysis[J]. Knowledge-Based Systems, 2016, 104:62-73.
[17] YAO Yiyu. Rough-set concept analysis: interpreting RS-definable concepts based on ideas from formal concept analysis[J]. Information Sciences, 2016, 346/347:442-462.
[18] 智慧来, 李金海. 基于必然属性分析的粒描述[J]. 计算机学报, 2018, 41(12):2702-2719. ZHI Huilai, LI Jinhai. Granule description based on necessary attribute analysis[J]. Chinese Journal of Computers, 2018, 41(12):2702-2719.
[19] YAO Yiyu. Interpreting concept learning in cognitive informatics and granular computing[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2009, 39(4):855-866.
[20] 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.
[21] LI Jinhai, MEI Changlin, XU Weihua, et al. Concept learning via granular computing: a cognitive viewpoint[J]. Information Sciences, 2015, 298:447-467.
[22] SHI Yong, MI Yunlong, LI Jinhai, et al. Concurrent concept-cognitive learning model for classification[J]. Information Sciences, 2019, 496:65-81.
[23] 李金海, 米允龙, 刘文奇. 概念的渐进式认知理论与方法[J]. 计算机学报, 2019, 42(10):2233-2250. LI Jinhai, MI Yunlong, LIU Wenqi. Incremental cognition of concepts: theories and methods[J]. Chinese Journal of Computers, 2019, 42(10):2233-2250.
[24] ZHANG Tao, LI Hehe, LIU Mengqi, et al. Incremental concept-cognitive learning based on attribute topology[J]. International Journal of Approximate Reasoning, 2020, 118:173-189.
[25] BELOHLAVEK R, DE BAETS B, KONECNY J. Granularity of attributes in formal concept analysis[J]. Information Sciences, 2014, 260:149-170.
[26] 李金海, 吴伟志, 邓硕. 形式概念分析的多粒度标记理论[J]. 山东大学学报(理学版), 2019, 54(2):30-40. LI Jinhai, WU Weizhi, DENG Shuo. Multi-scale theory in formal concept analysis[J]. Journal of Shandong University(Natural Science), 2019, 54(2):30-40.
[27] 李金海, 李玉斐, 米允龙, 等. 多粒度形式概念分析的介粒度标记方法[J]. 计算机研究与发展, 2020, 57(2):447-458. LI Jinhai, LI Yufei, MI Yunlong, et al. Meso-granularity labeled method for multi-granularity formal concept analysis[J]. Journal of Computer Research and Development, 2020, 57(2):447-458.
[28] 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.
[29] LIN T Y. Granular computing on binary relations I: data mining and neighborhood systems[C] //Rough Sets in Knowledge Discovery. Berlin: Springer, 1998: 107-121.
[30] YAO Yiyu. Information granulation and rough set approximation[J]. International Journal of Intelligent Systems, 2001, 16(1):87-104.
[31] 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. MIAO Duoqian, XU Feifei, YAO Yiyu, et al. Set-theoretic formulation of granular computing[J]. Chinese Journal of Computers, 2012, 35(2):2351-2363.
[32] 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):676-694. WANG Guoyin, ZHANG Qinghua, MA Xiao, et al. Granular computing models for knowledge uncertainty[J]. Journal of Software, 2011, 22(4):676-694.
[33] 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. LIANG Jiye, QIAN Yuhua, LI Deyu, et al. Theory and method of granular computing for big data mining[J]. Scientia Sinica Informationis, 2015, 45(11):1355-1369.
[34] YAO Yiyu. Three-way granular computing, rough sets, and formal concept analysis[J]. International Journal of Approximate Reasoning, 2020, 116:106-125.
[35] MA Jianmin, ZHANG Wenxiu, LEUNG Yee, et al. Granular computing and dual Galois connection[J]. Information Sciences, 2007, 177(23):5365-5377.
[36] WU Weizhi, LEUNG Yee, MI Jusheng. Granular computing and knowledge reduction in formal contexts[J]. IEEE Transactions on Knowledge and Data Engineering, 2009, 21(10):1461-1474.
[37] 陈德刚, 徐伟华, 李金海, 等. 粒计算基础教程[M]. 北京: 科学出版社, 2019. CHEN Degang, XU Weihua, LI Jinhai, et al. Elements of granular computing[M]. Beijing: Science Press, 2019.
[38] 张清华, 幸禹可, 王国胤. 概念知识粒与概念信息粒的相互转化[J]. 山东大学学报(理学版), 2010, 45(9):1-6. ZHANG Qinghua, XING Yuke, WANG Guoyin. Transformation between a concept knowledge granule and a concept information granule[J]. Journal of Shandong University(Natural Science), 2010, 45(9):1-6.
[39] WEI Ling, WAN Qing. Granular transformation and irreducible elements judgment based on pictorial diagrams[J]. IEEE Transactions on Cybernetics, 2016, 46(2):380-387.
[40] 米允龙,李金海,刘文奇,等. MapReduce框架下的粒概念认知学习系统研究[J].电子学报, 2018, 46(2):289-297. MI Yunlong, LI Jinhai, LIU Wenqi, et al. Research on granular concept cognitive learning system under MapReduce framework[J]. Acta Electronica Sinica, 2018, 46(2):289-297.
[41] 康向平, 苗夺谦. 基于粒计算的概念格拓展模型[J]. 同济大学学报(自然科学版), 2016, 44(7):1113-1120. KANG Xiangping, MIAO Duoqian. Expanded concept lattice based on granular computing[J]. Journal of Tongji University(Natural Science), 2016, 44(7):1113-1120.
[42] 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. LI Jinhai, WU Weizhi. Granular computing approach for formal concept analysis and its research outlooks[J]. Journal of Shandong University(Natural Science), 2017, 52(7):1-12.
[43] QIAN Yuhua, LIANG Jiye, YAO Yiyu, et al. MGRS: a multi-granulation rough set[J]. Information Sciences, 2010, 180(6):949-970.
[44] WU Weizhi, LEUNG Yee. Theory and applications of granular labeled partitions in multi-scale decision tables[J]. Information Sciences, 2011, 181(18):3878-3897.
[45] SHE Yanhong, HE Xiaoli, QIAN Ting, et al. A theoretical study on object-oriented and property-oriented multi-scale formal concept analysis[J]. International Journal of Machine Learning and Cybernetics, 2019, 10(11):3263-3271.
[46] QI Jianjun, WEI Ling, WAN Qing. Multi-level granularity in formal concept analysis[J]. Granular Computing, 2019, 4(3):351-362.
[47] 张文修, 仇国芳. 基于粗糙集的不确定决策[M]. 北京:清华大学出版社, 2005. ZHANG Wenxiu, QIU Guofang. Uncertain decision making based on rough sets[M]. Beijing: Tsinghua University Press, 2005.
[48] 刘之茗, 李金海. 多粒度形式背景的表示[J]. 海南热带海洋学院学报, 2019, 26(5):59-64. LIU Zhiming, LI Jinhai. The representation of multi-granularity formal contexts[J]. Journal of Hainan Tropical Ocean University, 2019, 26(5):59-64.
[49] QU Kaishe, ZHAI Yanhui, LIANG Jiye, et al. Study of decision implications based on formal concept analysis[J]. International Journal of General Systems, 2007, 36(2):147-156.
[50] 翟岩慧, 李德玉, 曲开社. 决策蕴涵规范基[J]. 电子学报, 2015, 43(1):18-23. ZHAI Yanhui, LI Deyu, QU Kaishe. Canonical basis for decision implications[J]. Acta Electronica Sinica, 2015, 43(1):18-23.
[1] HE Yi, SHAO Yabin, FENG Hui, GUO Ruilian. A classifier model based on the fast granular hypercube generation algorithm [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(5): 65-78.
[2] . Rotated granular support vector machine classifier algorithm [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(5): 102-113.
[3] HUA Youlin, SHAO Yabin, ZHU Xueqin. Multi-granularity support vector regression algorithm based on granular ball computing [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(7): 104-115.
[4] WU Hai, NIU Jiaojiao, TIE Wenyan, ZUO Jiankun. Concept lattice construction method based on granular concept network [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(12): 21-31.
[5] CHEN Yumin, ZHENG Guangyu, JIAO Na. Multi-label learning based on granular neural networks [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(5): 1-11.
[6] FAN Min, QIN Qin, LI Jinhai. Neighborhood recommendation algorithm based on three-way causality force [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(5): 12-22.
[7] ZHENG Chenying, CHEN Yingyue, HOU Xianyu, JIANG Lianji, LIAO Liang. A neighbourhood granular fuzzy C-means clustering algorithm [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(5): 35-44.
[8] WU Jiang, LIU Deshan,YU Yingying, PANG Kuo, LI Xiaofeng. Rule extraction based on linguistic concept lattice with fuzzy object [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(5): 63-69.
[9] FANG Fengqi, WU Weizhi. Knowledge reduction in decision set-valued systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(5): 82-89.
[10] Zhonghui LIU,Shuai JIANG,Fan MIN. Heuristic construction method of fuzzy concept set and its recommended application [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(3): 14-26.
[11] HAN Pei-lei, WEI Ling, WANG Zhen, ZHAO Si-yu. Complementary concepts and their properties and generation in FCA [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(8): 60-67.
[12] CHANG Li-na, WEI Ling. Rules acquisition based on OE-approximate concept lattice in incomplete formal decision contexts [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(11): 31-37.
[13] Jie TANG,Ling WEI,Rui-si REN,Si-yu ZHAO. Granule description using possible attribute analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(1): 75-82.
[14] LI Shuang-ling, YUE Xiao-wei, QIN Ke-yun. Granular structure in multi-source formal contexts [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 46-54.
[15] LIU Ying-ying, MI Ju-sheng, LIANG Mei-she, LI Lei-jun. Three-way interval-set concept lattice [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(3): 70-80.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd