JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (8): 60-67.doi: 10.6040/j.issn.1671-9352.0.2022.055

Previous Articles     Next Articles

Complementary concepts and their properties and generation in FCA

HAN Pei-lei1,2, WEI Ling1,2*, WANG Zhen1,2, ZHAO Si-yu1,2,3   

  1. 1. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China;
    2. Institute of Concepts, Cognition and Intelligence, Northwest University, Xian 710127, Shaanxi, China;
    3. School of Mathematics and Statistics, Xianyang Normal University, Xianyang 712000, Shaanxi, China
  • Online:2022-08-20 Published:2022-06-29

PDF (PC)

189

Abstract: In formal concept analysis, partial order relation of concept lattice describes generalization and specialization between concepts. There also exists some specific semantic information that is worth studying between incomparable concepts. Inspired by this, complementary concepts are studied in this paper. Firstly, the complementary degree of two object subsets is described by considering a specific attribute subset in formal context, based on which the strong and weak complementary relations are defined according to different actual needs. Further, the complementary concepts and their related properties are studied, and the optimal strong complementary concept and optimal weak complementary concept are explored under different semantics, and the corresponding algorithms are also given. Finally, examples are presented given to illustrate the rationality and applicability of the content of this paper.

Key words: concept lattice, formal concept analysis, strong complementary concept, weak complementary concept

CLC Number: 

  • TP18
[1] WILLE R. Restructuring lattice theory: an approach based on hierarchies of concepts[M] //RIVAL I. Ordered Sets. Dordrecht, Netherland: Springer, 1982: 445-470.
[2] GANTER B, WILLE R. Formal concept analysis: mathematical foundations[M]. New York: Springer-Verlag, 1999.
[3] KUZNETSOV S O, OBIEDKOV S A. Comparing performance of algorithms for generating concept lattices[J]. Journal of Experimental and Theoretical Artificial Intelligence, 2002, 14(2/3):189-216.
[4] 曾利程, 张祖平, 邹力耕. 增量式快速构建概念格算法[J]. 计算机科学与探索, 2018, 12(11):1862-1870. ZENG Licheng, ZHANG Zuping, ZOU Ligeng. Fast algorithm for incremental construction of concept lattice[J]. Journal of Frontiers of Computer Science and Technology, 2018, 12(11):1862-1870.
[5] QIAN Ting, WEI Ling, QI Jianjun. Constructing three-way concept lattices based on apposition and subposition of formal contexts[J]. Knowledge-Based Systems, 2017, 116:39-48.
[6] LIU Guilong. Attribute reduction algorithms determined by invariants for decision tables[J/OL]. Cognitive Computation, 2021[2022-02-23]. https://doi.org/10.1007/s12559-021-09887-w.
[7] ZHANG Wenxiu, WEI Ling, QI Jianjun. Attribute reduction theory and approach to concept lattice[J]. Science in China Series F: Information Science, 2005, 48(6):713-726.
[8] WANG Zhen, WEI Ling, QI Jianjun, et al. Attribute reduction of SE-ISI concept lattices for incomplete contexts[J]. Soft Computing, 2020, 24(20):15143-15158.
[9] 王振, 魏玲. 基于单边区间集概念格的不完备形式背景的属性约简[J]. 计算机科学, 2018, 45(1):73-78. WANG Zhen, WEI Ling. Attribute reduction of partially-known formal concept lattices for incomplete contexts[J]. Computer Science, 2018, 45(1):73-78.
[10] LI Jinhai, MEI Changlin, LV Yuejin. A heuristic knowledge-reduction method for decision formal contexts[J]. Computers and Mathematics with Applications, 2010, 61(4):1096-1106.
[11] LI Jinhai, MEI Changlin, LV Yuejin. Incomplete decision contexts: approximate concept construction, rule acquisition and knowledge reduction[J]. International Journal of Approximate Reasoning, 2013, 54(1):149-165.
[12] 朱治春, 魏玲. 基于类背景的双向规则的获取[J]. 西北大学学报(自然科学版), 2015, 45(4):517-524. ZHU Zhichun, WEI Ling. Two-way rules acquisition based on class contexts[J]. Journal of Northwest University(Natural Science Edition), 2015, 45(4):517-524.
[13] 李金海, 吕跃进. 基于概念格的决策形式背景属性约简及规则提取[J]. 数学的实践与认识, 2009, 39(7):182-188. LI Jinhai, LV Yuejin. Attribute reduction and rules extraction in decision formal context based on concept lattice[J]. Mathematics in Practice and Theory, 2009, 39(7):182-188.
[14] HU Zhiyong, SHAO Mingwen, LIU Huan, et al. Cognitive computing and rule extraction in generalized one-sided formal contexts[J/OL]. Cognitive Computation, 2021[2022-02-23]. https://doi.org/10.1007/s12559-021-09868-z.
[15] MISSAOUI R, GODIN R, BOUJENOUI A. Extracting exact and approximate rules from databases[C] // Proceedings of SOFTEKS Workshop on Incompleteness and Uncertainty in Information Systems. Berlin: Springer, 1993: 209-222.
[16] FREEMAN L C, WHITE D R. Using galois lattices to represent network data[J]. Sociological Methodology, 1993, 23:127-146.
[17] 崔晓婕, 许寒冰, 于微微, 等. 基于形式概念分析法研究针灸治疗肩痹选穴规律[J]. 世界中医药, 2021, 16(19):2941-2945. CUI Xiaojie, XU Hanbing, YU Weiwei, et al. Analysis on acupoint selection rules for treatment of shoulder arthralgia by acupuncture and moxibustion based on formal concept analysis[J]. World Chinese Medicine, 2021, 16(19):2941-2945.
[18] 张瑞玲, 徐红升, 沈夏炯. 基于偏序关系的子概念格判定算法[J]. 计算机应用与软件, 2008, 25(8):6-7, 64. ZHANG Ruiling, XU Hongsheng, SHEN Xiajiong. Determinant algorithm of sub-concept lattice on partial ordering relation basis[J]. Computer Applications and Software, 2008, 25(8):6-7, 64.
[19] 金岳霖. 形式逻辑[M]. 北京: 人民出版社, 1979: 34-41. JIN Yuelin. Formal logic[M]. Beijing: Peoples Publishing House, 1979: 34-41.
[20] 全国科学技术名词审定委员会. 资源科学技术名词[M]. 北京: 科学出版社, 2008: 203-204. China National Committee for Terminology in Science and Technology. Chinese terms in resource science and technology[M]. Beijing: Science Press, 2008: 203-204.
[21] QI Jianjun, WEI Ling, YAO Yiyu. Three-way formal concept analysis[C] // International Conference on Rough Sets and Knowledge Technology. Berlin: Springer, 2014: 732-741.
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[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 Fen-ning, FAN Min, LI Jin-hai. Dynamic updating of object-oriented granular concepts in formal concept analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(4): 105-115.
[8] 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.
[9] ZHANG En-sheng. Composition and structure on attribute reduction of interval-set concept lattices [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 17-24.
[10] 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.
[11] LI Jin-hai, WU Wei-zhi. Granular computing approach for formal concept analysis and its research outlooks [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 1-12.
[12] LIU Lin, WEI Ling, QIAN Ting. Three-way rules extraction in formal decision contexts with confidence [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 101-110.
[13] CHEN Xue, WEI Ling, QIAN Ting. Attribute reduction in formal decision contexts based on AE-concept lattices [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 95-103.
[14] QIN Li-zhen, LI Jin-hai, WANG Yang-yang. Concept lattice based knowledge discovery and its application to analysis of employment data in universities [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 58-64.
[15] TANG Ya-qiang, FAN Min, LI Jin-hai. Cognitive system model and approach to transformation of information granules under triadic formal concept analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(08): 102-106.
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] DONG Wei-wei. A new method of DEA efficiency ranking for decision making units with independent subsystems[J]. J4, 2013, 48(1): 89 -92 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd