JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (7): 37-43.doi: 10.6040/j.issn.1671-9352.4.2017.183

Previous Articles     Next Articles

Triadic concept analysis based on rough set theory

WANG Xia1,2, ZHANG Qian1, LI Jun-yu1,2, LIU Qing-feng3   

  1. 1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022, Zhejiang, China;
    2. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan 316022, Zhejiang, China;
    3. Department of Basic Teaching, Shandong Water Conservancy Vocational College, Rizhao 276826, Shandong, China
  • Received:2017-03-06 Online:2017-07-20 Published:2017-07-07

PDF (PC)

664

Abstract: Rough set approximation operators are introduced into triadic concept analysis to define object oriented triadic concepts and property oriented triadic concepts. Firstly, a possibility operator and a necessity operator are defined based on the ternary relation between the object set, attribute set and condition set of a triadic context. And properties of those two types of derivation operators are obtained. Then object oriented triadic concepts and property oriented triadic concepts are defined by using those two types of derivation operators. Finally, triadic diagrams are designed to describe all these object oriented triadic concepts and property oriented triadic concepts more directly.

Key words: triadic diagram, property oriented triadic concept, object oriented triadic concept, triadic context, rough set approximation operator

CLC Number: 

  • TP301
[1] GANTER B, WILLE R. Formal concept analysis mathematical foundations[M]. New York: Springer, 1999.
[2] WILLE R. Restructuring lattice theory: an approach based on hierarchies of concepts[M] // RIVAL I. Ordered Sets. Dordrecht: Reidel, 1982: 445-470.
[3] LEHMANN F, WILLE R. A triadic approach to formal concept analysis[C] // Conceptual Structures: Applications, Implementation and Theory. Heidelberg: Springer, 1995: 32-43.
[4] WEI Ling, QIAN Ting, WAN Qing, et al. A research summary about triadic concept analysis[J]. International Journal of Machine Learning and Cybernetics. DOI 10.1007/s13042-016-0599-7
[5] 魏玲, 万青, 钱婷, 等. 三元概念分析综述[J]. 西北大学学报(自然科学版), 2014, 44(5):689-699. WEI Ling, WAN Qing, QIAN Ting, et al. An overview of triadic concept analysis[J]. Journal of Northwest University(Natural Science Edition), 2014, 44(5):689-699.
[6] WILLE R. The basic theorem of triadic concept analysis[J]. Order, 1995, 12(2):149-158.
[7] BIEDERMANN K. Triadic Galois connections[M] // General algebra and applications in discrete mathematics.Aachen: ShakerVerlag, 1997: 23-33.
[8] BIEDERMANN K. An equational theory for trilattices[J]. Algebra Universalis, 1999, 42:253-268.
[9] BIEDERMANN K. How triadic diagrams represent conceptual structures[M] // Conceptual Structures: Fulfilling Peirces Dream(LNCS1257). Heidelberg: Springer, 1997: 304-317.
[10] GANTER B, OBIEDKOV S A. Implications in triadic formal contexts[M] // Conceptual Structures at Work(LNCS3127). Heidelberg: Springer, 2004: 186-195.
[11] MISSAOUI R, KWUIDA L. Mining triadic association rules from ternary relations[M] // Formal Concept Analysis(LNCS6628). Heidelberg: Springer, 2011: 204-218.
[12] DAU F, WILLE R. On the modal understanding of triadic context[M] // Classification and Information Processing at the Turn of the Millennium. Heidelberg: Springer, 2000: 83-94.
[13] JASCHKE R, HOTHO A, SCHMITZ C, et al. TRIAS-an algorithm for mining iceberg trilattices[C] // Proceeding of the Sixth International Conference on Data Mining. Berlin: Springer, 2006: 907-911.
[14] KAVTOUE M, KUZNETSOV S, MACKO J, et al. Minging Biclusters of similar values with triadic concept analysis[C] // Proceedings of the 7th International Conference on Concept Lattices and Their Applications. Berlin: Springer, 2011: 175-190.
[15] MEHDI KAYTOUE, SERGEI O. KUZNETSOV, et al. Biclustering meets triadic concept analysis. Annals of Mathematics and Artificial Intelligence[J]. Berlin: Springer, 2014,(70):55-79.
[16] BELOHLAVEK R, VYCHODIL V. Optimal factorization of three-way binary data[C] // Hu X, Lin T Y, Raghavan V, et al. 2010 IEEE International Conference on Granual Computing. Berlin: Springer, 2010: 61-66.
[17] GLODEANU C. Factorization methods of binary, triadic, real and fuzzy data[J]. Studia Universitatis Babes-Bolyai Series Informatica, 2011, 56(2):81-86.
[18] BELOHLAVEK R, GLODEANU C, VYCHODIL V. Optimal factorization of three-way binary data using triadic concepts[J]. Order, 2013, 30(2):437-454.
[19] CYNTHIA G. Tri-ordinal factor analysis[M] // CELLIER P, DISTEL F, GANTER B. Formal Concept Analysis. Heidelberg: Springer, 2013: 125-140.
[20] BELOHLAVEK R, OSICKA P. Triadic concept analysis of data with fuzzy attributes[C] // 2010 IEEE International Conference on Granular Computing. Berlin: Springer, 2010: 661-665.
[21] BELOHLAVEK R, OSICKA P. Triadic concept lattices of data with graded attributes[J]. International Journal of General System, 2012, 41(2):93-108.
[22] KONECNY J, OSICAKA P. Triadic concept lattices in the framework of aggregation structures [J]. Information Science, 2014, 279:512-527.
[23] GLODEANU C. Fuzzy-Valued triadic implications[C] // NAPOLI A, VYCHODIL V. Proceedings of the 7th International Conference on Concept Lattices and their Applications. Berlin: Springer, 2011: 159-173.
[24] BELOHLAVEK R, OSICKA P. Triadic fuzzy Galois connections as ordinary connections[J]. Fuzzy Sets and Systems, 2014, 249:83-99.
[25] GROH B, WILLE R. Lattices of Triadic Concept Graphs. Lecture Notes in Computer Science[M]. Berlin: Springer, 2000: 332-341.
[26] 汤亚强, 范敏, 李金海. 三元形式概念分析下的认知系统模型及信息粒转化方法[J]. 山东大学学报(理学版), 2014, 49(8):102-106. TANG Yaqiang, FAN Min, LI Jinhai. Cognitive system model and approach to transformation of information granules under triadic formal concept analysis[J]. Journal of Shandong University(Natural Science), 2014, 49(8):102-106.
[27] ROMAN Zhuk, IGNATOV Dmitry I, KONSTANTINOVA Natalia. Concept learning from triadic data[J]. Procedia Computer Science, 2014(31):928-938.
[28] FEI Hao, DOO-SOON Park, GEYONG Min, et al. K-cliques mining in dynamic social networks based on triadic formal concept analysis[J]. Neurocomputing, 2016(209):57-66.
[29] CH ASWANI Kumar, CHANDRA Mouliswaran S, LI Jinhai, et al. Role based access control design using Triadic concept analysis[J]. Journal of Central South University, 2016(23):3183-3191.
[30] GEDIGA G, DUNTSCH I. Modal-style operators in qualitative data analysis[C] // Proceedings of the 2002 IEEE International Conference on Data Mining. Berlin: Springer, 2002: 155-162.
[31] YAO Y Y. A comparative study of formal concept analysis and rough set theory in data analysis[C] // International Conference on Rough Sets and Current Trends in Computing. Berlin: Springer, 2004: 59-68.
[32] YAO Y Y. Concept lattices in rough set theory[C] // Proceedings of 23rd International Meeting of the North American Fuzzy Information Processing Society. Berlin: Springer, 2004: 796-801.
[1] LIU Li-zhao, YU Jia-ping, LIU Jian, LI Jun-yi, HAN Shao-bing, XU Hua-rong, LIN Huai-chuan, ZHU Shun-zhi. Secure storage addressing algorithm for large data based on quantum radiation field [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 65-74.
[2] SONG Xing-shen, YANG Yue-xiang, JIANG Yu. Efficient multiple sets intersection using SIMD instructions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(3): 54-62.
[3] . Graph model based trustworthy resource scheduling algorithm in cloud environment [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(1): 63-74.
[4] ZHU Dan, XIE Xiao-yao, XU Yang, XIA Meng-ting. Evaluation method for network security level based on cloud model and Bayesian feedback [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(1): 53-62.
[5] SHI Pei-yun, GAO Xing-bao. Individual strength-based multi-objective immune algorithm with adaptive differential evolution [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 1-10.
[6] WANG Feng, MAN Yuan, WANG Xing-le. N-shortest paths retrieval algorithm based on artificial immunity [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(9): 35-40.
[7] MA Lan, LI Wei-an, YIN Tian-yi. Improved particle swarm optimization for flight conflict resolution based on variable neighborhood search [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(1): 23-28.
[8] DU Hong-le, ZHANG Yan, ZHANG Lin. Intrusion detection on imbalanced dataset [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(11): 50-57.
[9] XIE Jian-min, YAO Bing, ZHAO Ting-gang. An algorithm and its implementation for odd-elegant labeling of general sun graph Sm,n [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 79-85.
[10] 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.
[11] LI Jing-wen, JIA Xi-bei, DONG Wei, LI Xiao-hui, YAN Guang-hui. The algorithm for adjacent-vertex-distinguishing total coloring of graphs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 14-21.
[12] ZHANG Chun-ying, WANG Li-ya, LIU Bao-xiang. Dynamic reduction theory for interval concept lattice based on covering and its realization [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(08): 15-21.
[13] LIU Jing-Lei, WANG Ling-Ling, ZHANG Wei. Generation algorithm for the role assigning lattice [J]. J4, 2009, 44(11): 52-56.
[14] QU Shouning, FU Aifang, LI Jing, LIU Jing. Forecasting stock market risks based on the flexible neural tree [J]. J4, 2009, 44(11): 44-47.
[15] YANG Yu-Zhen, LIU Pei-Yu, SHU Zhen-Fang, QIU Ye. Research of an improved information gain methodusing distribution information of terms [J]. J4, 2009, 44(11): 48-51.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd