JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (11): 31-37.doi: 10.6040/j.issn.1671-9352.4.2021.033

Previous Articles     Next Articles

Rules acquisition based on OE-approximate concept lattice in incomplete formal decision contexts

CHANG Li-na1,3*, WEI Ling2,3   

  1. 1. Department of Mathematics, Changzhi University, Changzhi 046011, Shanxi, China;
    2. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China;
    3. Institute of Concepts, Cognition and Intelligence, Northwest University, Xian 710127, Shaanxi, China
  • Online:2021-11-20 Published:2021-11-15

Abstract: First, OE-consistency of incomplete formal decision contexts is defined through the finer relation between the object-induced three-way condition approximate concept lattice and the object-induced three-way decision approximate concept lattice. Then, object induced three-way rules acquisition method is proposed based on the OE-consistent incomplete formal decision contexts, rules are acquired and interpreted from positive and negative perspectives respectively. Moreover, the judgement theorem of redundant rules and the extraction algorithm of irredundant rule sets are given. Finally, three-way rules acquisition method with confidence is proposed by using the inclusion degree theory, which provide more details and make the acquired rules more complete.

Key words: concept lattice, incomplete formal decision context, rules acquisition, consistency, object-induced three-way approximate concept

CLC Number: 

  • O29
[1] WILLE R. Restructuring lattice theory: an approach based on hierarchies of concepts[C] //RIVAL I Ordered Set. Dordrecht-Boston: Reidel, 1982: 445-470.
[2] GANTER B, WILLE R. Formal concept analysis: mathematical foundations[M]. Berlin: Springer-Verlag, 1999.
[3] XIE Junping, YANG Minhua, LI Jinhai, et al. Rule acquisition and optimal scale selection in multi-scale formal decision contexts and their applications to smart city[J]. Future Generation Computer Systems: FGCS, 2018, 83:564-581.
[4] 李金海,魏玲,张卓,等. 概念格理论与方法及其研究展望[J]. 模式识别与人工智能, 2020, 33(7):619-642. LI Jinhai, WEI Ling, ZHANG Zhuo, et al. Concept lattice theory and method and their research prospect[J]. Pattern Recognition and Artificial Intelligence, 2020, 33(7):619-642.
[5] BURMEISTER P, HOLZER R. On the treatment of incomplete knowledge in formal concept analysis[C] //Proceedings of 2000 International Conference on Conceptual Structures. Darmstadt: Springer, 2000: 385-398.
[6] DJOUADI Y, DUBOIS D, PRADE H. Differentes extensions floues de lanalyse formelle de concepts[C] //Rencontres Francophones sur la Logique Floue et ses Applications. Annecy: Springer, 2009: 141-148.
[7] 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.
[8] QI Jianjun, WEI Ling, YAO Yiyu. Three-way formal concept analysis[C] //International Conference on Rough Sets and Knowledge Technology. Cham: Springer, 2014: 732-741.
[9] QI Jianjun, QIAN Ting, WEI Ling. The connections between three-way and classical concept lattices[J]. Knowledge-Based Systems, 2016, 91:143-151.
[10] REN Ruisi, WEI Ling. The attribute reductions of three-way concept lattices[J]. Knowledge-Based Systems, 2016, 99:92-102.
[11] LI Meizeng, WANG Guoyin. Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts[J]. Knowledge-Based Systems, 2016, 91:165-178.
[12] YAO Yiyu. Interval sets and three-way concept analysis in incomplete contexts[J]. International Journal of Machine Learning & Cybernetics, 2017, 8(1): 3-20.
[13] WANG Zhen, WEI Ling, QI Jianjun, et al. Attribute reduction of SE-ISI concept lattices for incomplete contexts[J]. Soft Computing, 2020, 24:15143-15158.
[14] 魏玲. 粗糙集与概念格的约简理论与方法[D]. 西安: 西安交通大学, 2005. WEI Ling. Reduction theory and approach to rough set and concept lattice[D]. Xian: Xian Jiaotong University, 2005.
[15] 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.
[16] LI Jinhai, MEI Changlin, LV Yuejin. Knowledge reduction in decision formal contexts[J]. Knowledge-Based Systems, 2011, 24(5):709-715.
[17] LI Jinhai, MEI Changlin, ASWANI KUMAR C, et al. On rule acquisition in decision formal contexts[J]. International Journal of Machine Learning & Cybernetics, 2013, 4(6):721-731.
[18] ZHANG Shaoxia, LI Deyu, ZHAI Yanhui, et al. A comparative study of decision implication, concept rule and granular rule[J]. Information Sciences, 2020, 508:33-49.
[19] WEI Ling, LIU Lin, QI Jianjun, et al. Rules acquisition of formal decision contexts based on three-way concept lattices[J]. Information Sciences, 2020, 516:529-544.
[20] 祁建军, 魏玲, 姚一豫. 三支概念分析与决策[M]. 北京: 科学出版社, 2019. QI Jianjun, WEI Ling, YAO Yiyu. Three-way concept analysis and decisions[M]. Beijing: Science Press, 2019.
[21] 刘琳, 钱婷, 魏玲. 基于属性导出三支概念格的决策背景规则提取[J]. 西北大学学报(自然科学版), 2016, 46(4):481-487. LIU Lin, QIAN Ting, WEI Ling. Rules extraction in formal decision contexts based on attribute-induced three-way concept lattices[J]. Journal of Northwest University(Natural Science Edition), 2016, 46(4):481-487.
[22] 刘琳, 魏玲, 钱婷. 决策形式背景中具有置信度的三支规则提取[J]. 山东大学学报(理学版), 2017, 52(2):101-110. 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.
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] 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.
[7] 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.
[8] REN Rui-si, WEI Ling, QI Jian-jun. Rules acquisition on three-way weakly consistent formal decision contexts [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 76-85.
[9] LI Yong-ming, NIE Cai-ling, LIU Chao, GUO Jian-hua. Consistency of estimator of nonparametric regression function for arrays of rowwise NSD [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 69-74.
[10] 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.
[11] 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.
[12] HU Xue-ping, ZHANG Hong-mei. Convergence properties of the kernel-type density estimator under WOD dependent samples [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 21-25.
[13] 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.
[14] 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.
[15] LI Yong-ming, DENG Shao-jian, JIANG Wei-hong. Consistencies of recursive estimator of a probability density for extended negatively dependent samples [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 54-59.
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] 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 .
[7] 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 .
[8] 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 .
[9] DONG Wei-wei. A new method of DEA efficiency ranking for decision making units with independent subsystems[J]. J4, 2013, 48(1): 89 -92 .
[10] REN Min1,2, ZHANG Guang-hui1. Absorbing probabilities of random walks in an independent random  environment convergence in distribution on the half-line[J]. J4, 2013, 48(1): 93 -99 .