### F-C variable threshold concept lattices based on dependence spaces

ZHANG Jing, MA Jian-min*

1. School of Science, Changan University, Xian 710064, Shaanxi, China
• Published:2021-01-05

Abstract: For a fuzzy formal context, a congruence relation is defined based on a variable precision operator on the power set of attributes. A congruence relation is obtained. Based on it, a dependence space is shown. By constructing a closure operator according to the congruence relation, the relationships between the closure operator and the variable precision concepts are discussed. Furthermore, applying the properties of the closure operator, we get that any fixed point of the closure operator is exactly the intension of some variable precision concept. Based on these, an algorithm to construct all variable precision concepts is obtained. Experiments are used to verify the feasibility of the proposed method.

CLC Number:

• TP18
 [1] WILLE R. Restructuring lattice theory: an approach based on hierarchies of concepts[J]. Formal Concept Analysis, 1982, 5548(83):314-339.[2] GANTER B, WILLE R. Formal concept analysis: mathematical foundations[M]. New York: Springer-Verlag, 1999: 157-192.[3] JARVINEN J. Difference functions of dependences spaces[J]. Acta Cybernetica, 2001, 14(4):619-630.[4] ZOU Caifeng, DENG Huifang, WAN Jiafu, et al. Mining and updating association rules based on fuzzy concept lattice[J]. Future Generation Computer Systems, 2018, 82:698-706.[5] 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.[6] BURUSCO A, FUENTES R. The study of the L-fuzzy concept lattice[J]. Mathware and Soft Computing, 1994, 1(3):209-218.[7] BELOHLAVEK R. Concept lattices and order in fuzzy logic[J]. Annals of Pure and Applied Logic, 2004, 128(1):277-298.[8] ZHANG Wenxiu, MA Jianmin, FAN Shiqing. Variable threshold concept lattices[J]. Information Sciences, 2007, 177(22):4883-4892.[9] 仇国芳, 朱朝晖. 基于经典-模糊变精度概念格的决策规则获取及其推理算法[J]. 计算机科学, 2009, 36(12):216-218. QIU Guofang, ZHU Zhaohui. Acquisitions to decision rules and algorithms to inferences based on crisp-fuzzy variable threshold concept lattices[J]. Computer Science, 2009, 36(12):216-218.[10] YANG Yafeng. Parallel construction of variable precision concept lattice in fuzzy formal context[J]. AASRI Procedia, 2013, 5:214-219.[11] 范世青, 张文修. 模糊概念格与模糊推理[J]. 模糊系统与数学, 2006, 20(1):11-17. FAN Shiqing, ZHANG Wenxiu. Fuzzy concept lattice and fuzzy reasoning[J]. Fuzzy Systems and Mathematics, 2006, 20(1):11-17.[12] ZHUANG Ying, LIU Wenqi, WU Chinchia, et al. Pawlak algebra and approximate structure on fuzzy lattice[J]. The Scientific World Journal, 2014, 2014:697-706.[13] 崔芳婷, 王黎明, 张卓. 基于约束的模糊概念格构造算法[J]. 计算机科学, 2015, 42(8):288-293. CUI Fangting, WANG Liming, ZHANG Zhuo. Construction algorithm of fuzzy concept lattice based on constraints[J]. Computer Science, 2015, 42(8):288-293.[14] BOFFA S, MAIO C D, NOLA A D, et al. Unifying fuzzy concept lattice construction methods[C] //2016 IEEE International Conference on Fuzzy Systems(FUZZ-IEEE). [S.l] : IEEE, 2016.[15] PREM K, ASWANI C, LI Jinhai. Knowledge representation using interval-valued fuzzy formal concept lattice[J]. Soft Computing, 2016, 20(4):1485-1502.[16] MAO Hua, ZHENG Zhen. The construction of fuzzy concept lattice based on weighted complete graph[J]. Journal of Intelligent and Fuzzy Systems, 2019, 36(6):5797-5805.[17] 刘营营,米据生,梁美社,等. 三支区间集概念格[J]. 山东大学学报(理学版),2020, 55(3):70-80. LIU Yingying, MI Jusheng, LIANG Meishe, et al. Three-way interval-set concept lattice[J]. Journal of Shandong University(Natural Science), 2020, 55(3):70-80.[18] 林艺东, 李进金, 张呈玲. 基于矩阵的模糊-经典概念格属性约简[J]. 模式识别与人工智能, 2020, 33(1):21-31. LIN Yidong, LI Jinjin, ZHANG Chengling. Fuzzy-crisp concept lattice attribute reduction based on matrix[J]. Pattern Recognition and Artificial Intelligence, 2020, 33(1):21-31.[19] NOVOTNY M. Dependence spaces of information system[J]. Incomplete Information: Rough Set Analysis, 1998, 13:193-246.[20] MA Jianmin, ZHANG Wenxiu, WANG Xia. Dependence space of concept lattices based on rough set[C] //2006 IEEE International Conference on Granular Computing. Atlanta: IEEE, 2006: 200-204.[21] WANG Xia. Approaches to attribute reduction in concept lattices based on rough set theory[J]. International Journal of Hybrid Information Technology, 2012, 5(2):67-79.[22] 包永伟, 王霞, 吴伟志. 两类概念格的依赖空间理论[J]. 计算机科学, 2014, 41(2):236-239. BAO Yongwei, WANG Xia, WU Weizhi. Dependence space based on two types of concept lattices[J]. Computer Science, 2014, 41(2):236-239.[23] SHU Chang, MO Zhiwen, TANG Xiao, et al. Attribute reduction of lattice-value information system based on L-dependence spaces[J]. Fuzzy Information & Engineering and Operations Research & Management, 2014, 211:107-112.[24] MA Jianmin, ZHANG Wenxiu, CAI Sheng. Variable threshold concept lattice and dependence space[J]. Fuzzy Systems and Knowledge Discovery, 2006, 4223:109-118.[25] WARD M, DILWORTH R P. Residuated lattices[J]. Trans Amer Math Soc, 1939, 45:335-354.[26] 裴道武. 剩余格与正则剩余格的特征定理[J]. 数学学报, 2002, 45(2):271-278. PEI Daowu. The characterization of residuated lattices and regular residuated lattices[J]. Journal of Mathematics, 2002,45(2):271-278.[27] BURUSCO A, FUENTES R. The study on interval-valued contexts[J]. Fuzzy Sets and Systems, 2001, 121(3):439-452.
 [1] 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. [2] . The number of homomorphisms from metacyclic groups to metacyclic groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 17-22. [3] LU Tao, WANG Xi-juan, HE Wei. The operator theory on complete partially ordered objects in a topos [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 64-71. [4] BO Chun-xin, YAO Bing-xue. (λ, μ)-anti-fuzzy rough subgroup [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 23-27. [5] WEN Xian-hong, WU Hong-bo*. The prime reverse deductive system of locally finite #br# BL-algebras with properties [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(2): 36-41. [6] YU Cheng-yi, LI Jin-jin*. β lower approximation attribute reduction in variable precision rough sets [J]. J4, 2011, 46(11): 17-21. [7] LIU Lu-lu1, FU Wen-qing2, LI Sheng-gang1*. Characterizations of fuzzy subinclines, fuzzy ideals, fuzzy filters and fuzzy congruence relations [J]. J4, 2011, 46(11): 48-52. [8] LIU Chun-hui1, XU Luo-shan2. On ideals of residuated lattices [J]. J4, 2010, 45(4): 66-71. [9] ZHANG Yan-xia, LI Sheng-gang*, XIAN Lu. Products, sums, and quotients of M-closure spaces [J]. J4, 2010, 45(4): 74-76. [10] QIN Xue-cheng, LIU Chun-hui*. Fuzzy ⊙-ideals in regular residuated lattices [J]. J4, 2010, 45(10): 66-70.
Viewed
Full text

Abstract

Cited

Shared
Discussed