JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (8): 1-12.doi: 10.6040/j.issn.1671-9352.0.2022.066

    Next Articles

Cognition of network concepts based on variable precision possibility operator

FAN Min1,2, LUO Shan1,2, LI Jin-hai1,2*   

  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
  • Online:2022-08-20 Published:2022-06-29

Abstract: Concept cognition in a network is an important direction in the field of network data analysis. Starting from the necessity operator and possibility operator in formal concept analysis, this paper puts forward variable precision possibility operator, and illustrates that the classical possibility operators are special cases of the variable precision possibility operators. Furthermore, some properties of the possibility operators are studied, and their significances in the study of infectious disease networks are explained. Then, based on the variable precision possibility operators, two generalized network concepts and their upper approximations, lower approximations and boundary regions are proposed, and the upper and lower approximations and their boundary regions under variable precision possibility operators are illustrated to have much richer semantics through an example. After that, combined with the network eigenvalue method in complex network analysis, the network weak concepts are defined, and a network weak concept acquisition method based on variable precision possibility operator is presented. Finally, our algorithm is used to conduct some experiments on the UCI database, and the obtained results show that variable-precision possibility operators have advantages in network concept cognition.

Key words: concept cognition, formal context, network weak concept, necessity operator, variable precision possibility operator

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] GANTER B, WILLE R. Formal concept analysis: mathematical foundations[M]. New York: Springer-Verlag, 1999: 18-45.
[3] KUMAR C A, ISHWARYA M S, LOO C K. Formal concept analysis approach to cognitive functionalities of bidirectional associative memory[J]. Biologically Inspired Cognitive Architectures, 2015, 12:20-33.
[4] HAO Fei, YANG Yixuan, MIN Geyong, et al. Incremental construction of three-way concept lattice for knowledge discovery in social networks[J]. Information Sciences, 2021, 578:257-280.
[5] 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: 188-205. XU Weihua, LI Jinhai, WEI Ling, et al. Formal concept analysis: theory and application[M]. Beijing: Science Press, 2016: 188-205.
[6] 李进金,李克典,吴端恭. 基于粗糙集与概念格的知识系统模型[M]. 北京: 科学出版社, 2013: 119-142. LI Jinjin, LI Kedian, WU Duangong. Knowledge system model based on rough set and concept lattice[M]. Beijing: Science Press, 2013: 119-142.
[7] 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, 2003: 12-16. ZHANG Wenxiu, WU Weizhi, LIANG Jiye, et al. Rough set theory and methods[M]. Beijing: Science Press, 2003: 12-16.
[8] TONELLA P. Using a concept lattice of decomposition slices for program understanding and impact analysis[J]. IEEE Transactions on Software Engineering, 2003, 29(6):495-509.
[9] 朵琳,杨丙. 一种基于用户兴趣概念格的推荐评分预测方法[J]. 小型微型计算机系统, 2020, 41(10):2104-2108. DUO Lin, YANG Bing. Recommendation rating prediction based on user interest concept lattice[J]. Journal of Chinese Computer Systems, 2020, 41(10):2104-2108.
[10] ROCCO C M, HERNANDEZ-PERDOMO E, MUN J. Introduction to formal concept analysis and its applications in reliability engineering[J]. Reliability Engineering & System Safety, 2020, 202:107002.
[11] ANANIAS K, MISSAOUI R, RUAS P, et al. Triadic concept approximation[J]. Information Sciences, 2021, 572:126-146.
[12] ZOU Li, LIN Hongmei, SONG Xiaoying, et al. Rule extraction based on linguistic-valued intuitionistic fuzzy layered concept lattice[J]. International Journal of Approximate Reasoning, 2021, 133:1-16.
[13] ZOU Caifeng, DENG Huifang. Using fuzzy concept lattice for intelligent disease diagnosis[J]. IEEE Access, 2017, 5:236-242.
[14] CHEN Jianhong, ZHONG Xudong, XU Zitong, et al. Analysis of mine safety performance evaluation law based on matter-element analysis and rough set of concept lattice reduction[J]. IEEE Access, 2021, 9:94169-94180.
[15] DUNTSCH I, GEDIGA G. Modal-style operators in qualitative data analysis[C] //Proceedings of the 2002 IEEE International Conference on Data Mining. Washington, D.C.: IEEE, 2002: 155-162.
[16] YAO Yiyu. A comparative study of formal concept analysis and rough set theory in data analysis[C] //Proceedings of 4th International Conference on Rough Sets and Current Trends in Computing. Berlin: Springer, 2004: 59-68.
[17] 闫梦宇,李金海. 概念格共有与独有属性(对象)的关系研究[J]. 计算机科学与探索, 2019, 13(4):702-710. YAN Mengyu, LI Jinhai. Research on relationship between common and unique attributes(objects)of concept lattice[J]. Journal of Frontiers of Computer Science and Technology, 2019, 13(4):702-710.
[18] ZHAO Yingxiu, LI Jinhai, LIU Wenqi, et al. Cognitive concept learning from incomplete information[J]. International Journal of Machine Learning and Cybernetics, 2017, 7(4):159-170.
[19] LI Jinhai, HUANG Chenchen, QI Jianjun, et al. Three-way cognitive concept learning via multi-granularity[J]. Information Sciences, 2017, 378:244-263.
[20] QIAN Ting, WEI Ling, QI Jianjun. A theoretical study on the object(property)oriented concept lattices based on three-way decisions[J]. Soft Computing, 2019, 23(10):9477-9489.
[21] 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. Research on granular concept cognitive learning system under MapReduce framework[J]. Acta Electronica Sinica, 2018, 46(2):289-297.
[22] SHI Yong, MI Yunlong, LI Jinhai, et al. Concept-cognitive learning model for incremental concept learning[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(2):809-821.
[23] LI Jinhai, LIU Zhiming. Granule description in knowledge granularity and representation[J]. Knowledge-Based Systems, 2020, 203(11):106160.
[24] 林聚任. 社会网络分析: 理论、方法与应用[M]. 北京: 北京师范大学出版社, 2009: 306-307. LIN Juren. Social network analysis: theory, methods and applications[M]. Beijing: Beijing Normal University Publishing House, 2009: 306-307.
[25] PASTOR-SATORRAS R, CASTELLANO C, MIEGHEM P V, et al. Epidemic processes in complex networks[J]. Reviews of Modern Physics, 2015, 87(3):925-979.
[26] WATTS D J, STROGATZ S H. Collective dynamics of ‘small-world’ networks[J]. Nature, 1998, 393(6684):440-442.
[27] BARABÁSI A L, ALBERT R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439):509-512.
[28] SHARMA N, VERMAC A K, GUPTAA A K. Spatial network based model forecasting transmission and control of COVID-19[J]. Physica A: Statistical Mechanics and its Applications, 2020, 581:126223.
[29] MARON B A, ALTUCCI L, BALLIGAND J L, et al. A global network for network medicine[J]. NPJ Systems Biology and Applications, 2020, 6:29.
[30] PAUL A, BHATTACHARJEE J K, PAL A, et al. Emergence of universality in the transmission dynamics of COVID-19[J]. Scientific Reports, 2021, 11:18891.
[31] GYSI D M, VALLE T D, ZITNIK M, et al. Network medicine framework for identifying drug-repurposing opportunities for COVID-19[J]. Proceedings of the National Academy of Sciences, 2021, 118(19):e2025581118.
[32] KERMACK W O, MCKENDRICK A G. A contribution to the mathematical theory of epidemics[J]. Proceedings of the Royal Society of London Series A, 1927, 115(772):700-721.
[33] ROMAN H E, CROCCOLO F. Spreading of infections on network models: percolation clusters and random trees[J]. Mathematics, 2021, 9(23):1-22.
[34] PASTOR-SATORRAS R, VESPIGNANI A. Immunization of complex networks[J]. Physical Review E, 2001, 65(3):036104.
[35] BOGUN A M, PASTOR-SATORRAS R. Epidemic spreading in correlated complex networks[J]. Physical Review E, 2002, 66(4):047104.
[36] LEVENTHAL G E, HILL A L, NOWAK M A, et al. Evolution and emergence of infectious diseases in theoretical and real-world networks[J]. Nature Communications, 2015, 6:6101.
[37] SCARPINO S V, PETRI G. On the predictability of infectious disease outbreaks[J]. Nature Communications, 2019, 10:898.
[38] ZHANG Yuexia, PAN Dawei. Layered SIRS model of information spread in complex networks[J]. Applied Mathematics and Computation, 2021, 411:126524.
[39] 马娜,范敏,李金海. 复杂网络下的概念认知学习[J]. 南京大学学报(自然科学), 2019, 55(4):609-623. MA Na, FAN Min, LI Jinhai. Concept-cognitive learning under complex network[J]. Journal of Nanjing University(Natural Science), 2019, 55(4):609-623.
[40] 刘文星,范敏,李金海. 网络形式背景下的社区划分方法研究[J]. 计算机科学与探索, 2021, 15(8):1441-1449. LIU Wenxing, FAN Min, LI Jinhai. Research on community division method under network formal context[J]. Journal of Frontiers of Computer Science and Technology, 2021, 15(8):1441-1449.
[1] Jing ZHANG,Jian-min MA. F-C variable threshold concept lattices based on dependence spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(1): 68-74.
[2] XIE Xiao-xian, LI Jin-jin, CHEN Dong-xiao, LIN Rong-de. Concept reduction of preserving binary relations based on Boolean matrix [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 32-45.
[3] CHEN Dong-xiao, LI Jin-jin, LIN Rong-de, CHEN Ying-sheng. Rough approximation in multi-scale formal context [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 22-31.
[4] 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.
[5] LI Jin-hai, HE Jian-jun, WU Wei-zhi. Optimization of class-attribute block in multi-granularity formal concept analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(5): 1-12.
[6] JI Ru-ya, WEI Ling, REN Rui-si, ZHAO Si-yu. Pythagorean fuzzy three-way concept lattice [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(11): 58-65.
[7] LI Jin-hai, WU Wei-zhi, DENG Shuo. Multi-scale theory in formal concept analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(2): 30-40.
[8] QIAN Ting, ZHAO Si-yu, HE Xiao-li. Rules acquisition of decision formal contexts based on attribute granular [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(10): 113-120.
[9] HUANG Tao-lin, NIU Jiao-jiao, LI Jin-hai. Reduct updating method in a dynamic formal context based on granular discernibility attribute matrix [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 13-21.
[10] LING Mi-ran, MI Ju-sheng, MA Li. Heterogeneous formal contexts for uncertainty reasoning [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(08): 28-32.
[11] WANG Bin-di, WEI Ling. The reduction theory of concept lattice based on its associated lattice [J]. J4, 2010, 45(9): 20-26.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] YANG Jun. Characterization and structural control of metalbased nanomaterials[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 1 -22 .
[2] HE Hai-lun, CHEN Xiu-lan* . Circular dichroism detection of the effects of denaturants and buffers on the conformation of cold-adapted protease MCP-01 and  mesophilic protease BP01[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 23 -29 .
[3] ZHAO Jun1, ZHAO Jing2, FAN Ting-jun1*, YUAN Wen-peng1,3, ZHANG Zheng1, CONG Ri-shan1. Purification and anti-tumor activity examination of water-soluble asterosaponin from Asterias rollestoni Bell[J]. J4, 2013, 48(1): 30 -35 .
[4] SUN Xiao-ting1, JIN Lan2*. Application of DOSY in oligosaccharide mixture analysis[J]. J4, 2013, 48(1): 43 -45 .
[5] LUO Si-te, LU Li-qian, CUI Ruo-fei, ZHOU Wei-wei, LI Zeng-yong*. Monte-Carlo simulation of photons transmission at alcohol wavelength in  skin tissue and design of fiber optic probe[J]. J4, 2013, 48(1): 46 -50 .
[6] YANG Lun, XU Zheng-gang, WANG Hui*, CHEN Qi-mei, CHEN Wei, HU Yan-xia, SHI Yuan, ZHU Hong-lei, ZENG Yong-qing*. Silence of PID1 gene expression using RNA interference in C2C12 cell line[J]. J4, 2013, 48(1): 36 -42 .
[7] MAO Ai-qin1,2, YANG Ming-jun2, 3, YU Hai-yun2, ZHANG Pin1, PAN Ren-ming1*. Study on thermal decomposition mechanism of  pentafluoroethane fire extinguishing agent[J]. J4, 2013, 48(1): 51 -55 .
[8] YANG Ying, JIANG Long*, SUO Xin-li. Choquet integral representation of premium functional and related properties on capacity space[J]. J4, 2013, 48(1): 78 -82 .
[9] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors[J]. J4, 2013, 48(1): 83 -88 .
[10] SHI Kai-quan. P-information law intelligent fusion and soft information #br# image intelligent generation[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(04): 1 -17 .