Computer Science

Computer Science ›› 2025, Vol. 52 ›› Issue (6): 151-158.doi: 10.11896/jsjkx.240600055

• Database & Big Data & Data Science • Previous Articles     Next Articles

Relationship Between Triadic Concept Reducts and Concept Reducts

LI Xuan1,3, ZHANG Qin1,3, WEI Ling1,2,3   

  1. 1 School of Mathematics,Northwest University,Xi'an 710127,China
    2 School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China
    3 Institute of Concepts,Cognition and Intelligence,Northwest University,Xi'an 710127,China
  • Received:2024-06-06 Revised:2024-08-26 Online:2025-06-15 Published:2025-06-11
  • About author:LI Xuan,born in 1999,master.Her main research interests include formal concept analysis,three-way decision and granular computing.
    WEI Ling,born in 1972.Ph.D,professor,Ph.Dsupervisor.Her main research interests include formal concept analysis,rough set,three-way decision and granular computing.
  • Supported by:
    National Natural Science Foundation of China(12171392),Shaanxi Fundamental Science Research Project for Mathematics and Physics(23JSZ008) and Graduate Innovation Fund of Northwest University(CX2024128).

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Abstract: Triadic concept analysis is an extension of formal concept analysis,and the ternary relation reflected in the triadic context corresponds to the binary relation based on the condition,so there is a close connection between the concept reduction that keeps the binary relation unchanged and the triadic concept reduction that keeps the ternary relation unchanged.Based on this,the relationship between concept reducts and triadic concept reducts is investigated.Firstly,the data under each condition in the tri-adic context is regarded as a formal context,and according to the relationship between formal concepts and triadic concepts,it is proved that the sets formed by the concept reducts of all conditionally determined formal contexts can generate triadic concept consistent sets.Secondly,using the set formed by triadic concepts according to the same conditions can get the set of concepts under the corresponding conditions.It is further proved that the concept consistent sets of formal contexts determined by all conditions can be generated from triadic concept reducts,and the equivalent proposition that triadic concept reducts and concept reducts are generated by each other is given.Finally,the relationship between the three types of formal concepts and the three types of triadic concepts is discussed with respect to the three types of concepts that play different roles in concept reducts and triadic concept reducts.

Key words: Triadic context, Triadic concept, Formal concept, Concept reduction, Triadic concept reduction

CLC Number: 

  • O29
[1]WILLE R.Restructuring lattice theory:An approach based on hierarchies of concepts [C]//Ordered Sets.Dordrecht-Boston:Springer,1982:445-470.
[2]GANTER B,WILLE R.Formal concept analysis:Mathematical foundations [M].Berlin:Springer,1999.
[3]YAN M Y,LI J H.Knowledge discovery and updating under the evolution of network formal contexts based on three-way decision [J].Information Sciences,2022,601:18-38.
[4]XU W H,YANG L,ZHANG X Y.Fuzzy three-way formal concept analysis and concept-cognitive learning [J].Journal of Northwest University(Natural Science Edition),2020,50(4):516-528.
[5]MAKHALOVA T,BUZMAKOV A,KUZNETSOV S O,et al.Introducing the closure structure and the GDPM algorithm for mining and understanding a tabular dataset [J].International Journal of Approximate Reasoning,2022,145:75-90.
[6]ZHANG W X,WEI L,QI J J.Attribute reduction theory andapproach to concept lattice [J].Science in China Series F-Information Sciences,2005,48(6):713-726.
[7]WANG X,MA J M.A novel approach to attribute reduction in concept lattices [C]//Proceedings of the 1st International Conference on Rough Sets and Knowledge Technology.Berlin,Heidelberg:Springer,2006:522-529.
[8]LI T J,LI M Z,GAO Y.Attribute reduction of concept latticebased on irreducible elements [J].International Journal of Wavelets Multiresolution and Information Processing,2013,11(6):2792-2813.
[9]WU W Z,LEUNG Y,MI J S.Granular computing and knowledge reduction in formal contexts [J].IEEE Transactions on Knowledge and Data Engineering,2009,21(10):1461-1474.
[10]CAO L,WEI L,QI J J.Concept reduction preserving binary relations [J].Pattern Recognition and Artificial Intelligence,2018,31(6):516-524.
[11]WEI L,CAO L,QI J J,et al.Concept reduction and conceptcharacteristics in formal concept analysis [J].Scientia Sinica Informationis,2020,50(12):1817-1833.
[12]XIE X X,LI J J,CHEN D X,et al.Concept reduction of preserving binary relations based on boolean matrix [J].Journal of Shandong University(Natural Science Edition),2020,55(5):32-45.
[13]WANG X,PENG Z H,LI J Y,et al.Method of concept reduction based on concept discernibility matrix [J].Computer Science,2021,48(1):125-130.
[14]ZHAO S Y,QI J J,LI J A,et al.Concept reduction in formal concept analysis based on representative concept matrix [J].International Journal of Machine Learning and Cybernetics,2023,14(4):1147-1160.
[15]MA W S,HOU X L.Same effect relation and concept reduction in formal concept analysis [J].Computer Science,2023,50(4):63-76.
[16]WEI L,ZHAO S Y,QI J J.Symmetric formal context and its concept reduct [J].Journal of Northwest University(Natural Science Edition),2023,53(5):794-802.
[17]LI Y,ZHAO S Y,REN R S,et al.Concept reduction preserving antecedentinformation of rules [J].Journal of Northwest University(Natural Science Edition),2023,53(5):803-811.
[18]YU Y Q,ZHAO S Y,WEI L.Concept reduction of property-oriented concept lattices and its application in knowledge space theory [J].Journal of Northwest University(Natural Science Edition),2023,53(5):812-820.
[19]ZHU D D,REN R S,ZHAO S Y,et al.Three types of SE-ISI concept reduction based on incomplete contexts [J].Journal of Northwest University(Natural Science Edition),2023,53(5):821-829.
[20]LEHMANN F,WILLE R.A triadic approach to formal concept analysis [C]//Proceedings of the 3rd International Conference on Conceptual Structures:Applications,Implementation and Theory.Berlin:Springer,1995:32-43.
[21]WILLE R.The basic theorem of triadic concept analysis [J].Order,1995,12(2):149-158.
[22]BIEDERMANN K.Triadic Galois connections[G]//General Al-gebra and Applications in Discrete Mathematics.Aachen:Shaker Verlag,1997:23-33.
[23]BIEDERMANN K.An equational theory for trilattices [J].Algebra Universalis,1999,42(4):253-268.
[24]GANTER B,OBIEDKOV S A.Implications in triadic formalcontexts [C]//Proceeding of the 12th International Conference on Conceptual Structures.Berlin:Springer,2004:186-195.
[25]MISSAOUI R,KWUIDA L.Mining triadic association rulesfrom ternary relations [C]//Proceeding of the 9th International Conference on Formal Concept Analysis.Berlin:Springer,2011:204-218.
[26]BELOHLAVEK R,GLODEANU C,VYCHODIL V.Optimalfactorization of three-way binary data using triadic concepts [J].Order,2013,30(2):437-454.
[27]CYNTHIA G.Tri-ordinal factor analysis [C]//Proceeding ofthe 11th International Conference on Formal Concept Analysis.Berlin:Springer,2013:125-140.
[28]WEI L,WAN Q,QIAN T,et al.A research summary about triadic concept analysis [J].Journal of Northwest University(Natural Science Edition),2014,44(5):689-699.
[29]WANG X,JIANG S,LI J Y,et al.A construction method of triadic concepts [J].Journal of Computer Research and Development,2019,56(4):844-853.
[30]WANG X,QUAN Y,LI J Y,et al.Incremental constructionmethod of triadic concepts [J].Journal of NanJing University(Natural Science Edition),2022,58(1):19-28.
[31]WANG X,LI J Y,WU W Z.Booleanmatrix representation oftriadic concepts [J].Computer Science,2023,50(6):109-115.
[32]BAZIN A.A triadic generalisation of the boolean concept lattice [C]//Proceeding of the 17th International Conference on Formal Concept Analysis.Cham:Springer,2023:95-105.
[33]WEI L,CAO L,QI J J.Reduction based on the binary relations for triadic contexts [J].Journal of Northwest University(Natural Science Edition),2017,47(3):313-320.
[34]QI J J,WEI L.Simplification of triadic contexts and concept trilattices [J].Computer Science,2017,44(9):53-57.
[35]LI J Y,LI X X,WANG X,et al.Reduction of triadic concepts based on triadic factor analysis [J].Journal of Nanjing University(Natural Science Edition),2020,56(4):480-493.
[36]LI J Y,ZHU R J,WANG X,et al.The relationship between triadic concepts and formal concepts [J].Journal of NanJing University(Natural Science Edition),2018,54(4):786-793.
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