Computer Science ›› 2017, Vol. 44 ›› Issue (9): 53-57.doi: 10.11896/j.issn.1002-137X.2017.09.010

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Simplification of Triadic Contexts and Concept Trilattices

QI Jian-jun and WEI Ling   

  • Online:2018-11-13 Published:2018-11-13

Abstract: Triadic concept analysis (TCA) is an extension of formal concept analysis (FCA).As the data foundation,the triadic contexts is commonly used in the real world.The ternary relationship shown in a triadic context is the base to forming concept trilattice,it is more complicated than binary relationship shown in a formal context.It results in intrication of triadic concepts and concept trilattices.Aiming to the information simplification of a concept trilattice,an approach to simplifying a triadic context and its concept trilattice on the basis of binary relationship was proposed,since the binary relationship is essential to some extent.The main idea is to delete the redundant elements in each universe while keeping all the binary relationship of the original triadic context.Actually,three universes of a triadic context can be considered at the same time using this method.After the simplification,we obtained some properties about the simplified concept trilattice,and we also discussed the relationship between former triadic concept and later triadic concept.These conclusions are research basis for the future algorithm research and application,also the base for the deeper theoretic study.

Key words: Triadic concept analysis,Triadic context,Triadic concept,Concept trilattice,Simplification

[1] GANTER B,WILLE R.Formal Concept Analysis-Mathematical Foundations[M].New York:Springer Berlin Heidelberg,1999.
[2] WILLE R.Restructuring lattice theory:an approach based onhierarchies of concepts[M]∥Rival I.Ordered Sets.Dordrecht:Reidel,1982:445-470.
[3] CH S.Peirce:Collected Papers[M].Cambridge:Harvard Univ.Press,1931-1935.
[4] LEHMANN F,WILLE R.A triadic approach to formal concept analysis[M]∥Ellis G,Levinson R,Rich W,et al.Conceptual Structures:Applications,Implementation and Theory (LNCS 954).Heidelberg:Springer,1995:32-43.
[5] WILLE R.The basic theorem of triadic concept analysis[J].Order,1995,12(2):149-158.
[6] BIEDERMANN K.Triadic Galois connections [M]∥Denecke K,Lders.General algebra and applications in discrete mathema-tics.Aachen:Shaker Verlag,1997:23-33.
[7] BIEDERMANN K.An equational theory for trilattices [J].Algebra Universalis,1999(42):253-268.
[8] GANTER B,OBIEDKOV S.Implications in triadic formal contexts [M]∥Wolff K E,Pfeiffer H D,Delugach H S.Conceptual Structures at Work(LNCS3127).Heidelberg:Springer,2004:186-195.
[9] MISSAOUI R,KWUIDA L.Mining triadic association rulesfrom ternary relations [M]∥Valtchev P,Jaschke R.International Conference on Formal Concept Analysis (LNCS6628).Heidelberg:Springer,2011:204-218.
[10] JASCHKE R,HOTHO A,SCHMITZ C,et al.TRIAS-an algorithm for mining iceberg tri-lattices[C]∥Proceeding of the sixth international conference on data mining (ICDM’06).Piscataway,Null,IEEE,2006:907-911.
[11] IGNATOV D,KUZNETSOV S,MAGIZOV R,et al.From tri-concepts to triclusters [M]∥Kuznetsov S O,et al.Rough Sets,Fuzzy Sets,Data Mining and Granular Computing,RSFDGrC 2011(LNCS6743).Heidelberg:Springer,2011:257-264.
[12] KAYTOUE M,KUZNETSOV S,MAGIZOV J,et al.Mining Bi-clusters of similar values with triadic concept analysis [C]∥Napoli A,Vychodil V.Proceedings of the 7th International Confe-rence on Concept Lattices and Their Applications (CLA2011).2011:175-190.
[13] GNATYSHAK D,IGNATOV D,SEMENOV A,et al.Gaining insight in social networks with biclustering and triclustering [M]∥Aseeva N,Babkin E,Kozyrev O.Perspectives in Business Informatics Research (LNBIP128).Heidelberg:Springer,2012:162-171.
[14] 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 Granular Computing.Piscataway,NJ:IEEE,2010:61-66.
[15] GLODEANU C.Factorization methods of binary,triadic,realand fuzzy data [J].Studia Universitatis Babes-Bolyai Series Informatica,2011,56(2):81-86.
[16] BELOHLAVEK R,GLODEANU C,VYCHODIL V.Optimalfactorization of three-way binary data using triadic concepts [J].Order,2013,30(2):437-454.
[17] CYNTHIA G.Tri-ordinal factor analysis [M]∥Cellie R P,Distel F,Ganter B.Formal Concept Analysis (LNCS7880).Heidelberg:Springer,2013:125-140.
[18] BELOHLAVEK R,OSICKA P.Triadic concept analysis of data with fuzzy attributes [C]∥2010 IEEE International Conference on Granular Computing.Piscataway,NJ:IEEE,2010:661-665.
[19] OSICKA P,KONECNY J.General approach to triadic conceptanalysis [C]∥Kryszkiewicz M,Obiedkov S.Proceedings of the 7th International Conference on Concept Lattices and Their Applications (CLA2010).2010:116-126.
[20] BELOHLAVEK R,OSICKA P.Triadic concept lattices of data with graded attributes [J].International Journal of General System,2012,41(2):93-108.
[21] KONECNY J,OSICKA P.Triadic concept lattices in the framework of aggregation structures [J].Information Science,2014,279:512-527.
[22] GLODEANU C V.Fuzzy-Valued triadic implications [C]∥Napoli A,Vychodil V.Proceedings of the 7th International Confe-rence on Concept Lattices and Their Applications (CLA2011).2011:159-173.
[23] BELOHLAVEK R,OSICKA P.Triadic fuzzy Galois connections as ordinary connections [J].Fuzzy Sets and Systems,2014,249:83-99.
[24] OSICKA P.Algorithms for computation of concept trilattices of triadic fuzzy context [M]∥Greco S,Meunier B B,Coletti G,et al.Advances in Computational Intelligence (CCIS 299).Heidelberg:Springer,2012:221-230.
[25] TRABELSI C,JELASSI N,YAHIA S.Scalable mining of fre-quent tri-concepts from folksonomies [M]∥Tan P N,Chawla S,Ho C K,et al.Advances in Knowledge Discovery and Data Mining (LNCS7302).Heidelberg:Springer,2012:231-244.
[26] JELASSI M N,YAHIA S B,NGUIFO E M.A scalable mining of frequent quadratic concepts in d-folksonomies[J].Computer Science,2012.arXiv:1212.0087v1 [cs.SI].
[27] WEI L,WAN Q,QIAN T,et al.An Overview of Triadic Concept Analysis[J].Journal of Northwest University (NaturalScience Edition),2014,44(5):689-699.(in Chinese) 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.

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