《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (3): 70-80.

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### 三支区间集概念格

1. 1.河北师范大学数学与信息科学学院, 河北 石家庄 050024;2.石家庄职业技术学院, 河北 石家庄 050081
• 发布日期:2020-03-27
• 作者简介:刘营营(1994— ), 女, 硕士研究生, 研究方向为人工智能数学基础. E-mail:15732155710@163.com*通信作者简介:米据生(1966— ), 男, 博士, 教授, 博导,研究方向为人工智能数学基础. E-mail:mijsh@263.net
• 基金资助:
国家自然科学基金资助项目(61573127,61502144);河北省自然科学基金资助项目(F2018205196);河北省高等学校科学技术研究项目(BJ2019014,QN2017095);河北省博士后择优资助科研项目(B2016003013);河北省“三三三人才工程”培养经费资助项目(A2017002112);河北师范大学博士基金项目(L2017B19);河北师范大学硕士研究生创新项目(CXZZSS2019062)

### Three-way interval-set concept lattice

LIU Ying-ying1, MI Ju-sheng1*, LIANG Mei-she1,2, LI Lei-jun1

1. 1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, Hebei, China;
2. Shijiazhuang University of Applied Technology, Shijiazhuang 050081, Hebei, China
• Published:2020-03-27

Abstract: This paper respectively proposes a three-way interval-set concept lattice model in complete and incomplete formal context, and systematically analyses the connections between the object-induced three-way interval-set concept lattice and the interval-set concept lattice. In addition, the necessary and sufficient conditions for constructing the object-induced three-way interval-set concept on the basis of the interval-set concept are proved, and the corresponding algorithm is formulated. Finally, the relationships between the object-induced three-way interval-set concept and the interval-set concept are studied. The necessary and sufficient conditions for constructing the object-induced three-way interval-set concept on the basis of the classical concept are proved.

• O236
 [1] WILLE R. Restructuring lattice theory: an approach based on hierarchies of concept[M]. Reidel: Dordrecht-Boston, 1982: 445-470.[2] GANTER B, WILLE R. Formal concept analysis: mathematical foundations[M]. Berlin: Springer, 1999: 79-90.[3] YAO Yiyu. Interval-set algebra for qualitative knowledge representation[C] // Proceedings of the 5th International Conference on Computing and Information. Washington: IEEE, 1993: 370-375.[4] 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: 69-88. XU Weihua, LI Jinhai, WEI Ling, et al. The formal concept analysis: theory and application[M]. Beijing: Science Press, 2016: 69-88.[5] YAO Yiyu. Interval sets and three-way concept analysis in incomplete contexts[J]. International Journal of Machine Learning and Cybernetics, 2017, 8(1):3-20.[6] 钱婷, 贺晓丽. 区间集概念格的构造理论研究[J]. 西北大学学报(自然科学版), 2017, 47(3):330-335. QIAN Ting, HE Xiaoli. The construction theoretical research of interval-set concept lattice[J]. Journal of Northwest University(Natural Science), 2017, 47(3):330-335.[7] 张恩胜. 区间集概念格属性约简的组成与结构[J]. 山东大学学报(理学版), 2018, 53(8):17-24. ZHANG Ensheng. Composition and structure on attribute reduction of interval-set concept lattices[J]. Journal of Shandong University(Natural Science), 2018, 53(8):17-24.[8] YU Huiying, LI Qingguo, CAI Mingjie. Characteristics of three-way concept lattice and three-way rough concept lattice[J]. Knowledge-Based Systems, 2018, 146:181-189.[9] FENG Tao, FAN Huitao, MI Jusheng. Uncertainty and reduction of variable precision multigranulation fuzzy rough sets based on three-way decisions[J]. International Journal of Approximate Reasoning, 2017, 85:36-58.[10] 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.[11] QI Jianjun, WEI Ling, YAO Yiyu. Three-way formal concept analysis[J]. Lecture Notes in Computer Science, 2014, 8818:732-741.[12] LI Meizheng, WANG Guoyin. Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts[J]. Knowledge-Based Systems, 2016, 91:165-178.[13] WEI Ling, QIAN Ting. The three-way object oriented concept lattice and the three-way property oriented concept lattice[C] // 2015 International Conference on Machine Learning and Cybernetics, Guangzhou: IEEE, 2015: 854-859.[14] REN Ruisi, WEI Ling. The attribute reductions of three-way concept lattice[J]. Knowledge-Based Systems, 2016, 99:92-102.[15] QI Jianjun, QIAN Ting, WEI Ling. The connections between three-way and classical concept lattice[J]. Knowledge-Based Systems, 2016, 91:143-151.[16] 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.[17] MI Jusheng, YEE Leung, WU Weizhi. Approaches to attribute reduction in concept lattice induced by axialities[J]. Knowledge-Based Systems, 2010, 23(6):504-511.[18] 胡谦, 米据生, 李磊军. 多粒度模糊粗糙近似算子的信任结构与属性约简[J]. 山东大学学报(理学版), 2017, 52(7):30-36. HU Qian, MI Jusheng, LI Leijun. The fuzzy belief structure and attribute reduction based on multi-granulation fuzzy rough operators[J]. Journal of Shandong University(Natural Science), 2017, 52(7):30-36.[19] KONECNY J. On efficient factorization of standard fuzzy concept lattice and attribute-oriented fuzzy concept lattice[J]. Fuzzy Sets and Systems, 2018, 351:108-121.[20] EDUARD B, JAN K. L-concept lattices with positive and negative attributes: modeling uncertainty and reduction of size[J]. Information Sciences, 2019, 472:163-179.[21] CIOBANU G, VĂIDEANU C. A note on similarity relations between fuzzy attribute-oriented concept lattices[J]. Information Sciences, 2018, 460/461:254-263.
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