A new algebraic structure for formal concept analysis

Information Sciences

Volumn 180, Issue 24, 2010, Pages 4865-4876

  Wang, Lidong ^a   Liu, Xiaodong ^a,b   Cao, Jiannong ^c  

^a DALIAN MARITIME UNIVERSITY   (China)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^c HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

Algebraic structure; Concept lattice; Formal concept; Ontology merging

Indexed keywords

ALGEBRA SYSTEMS; ALGEBRAIC STRUCTURES; CONCEPT HIERARCHIES; CONCEPT LATTICES; DATA ANALYSIS; FORMAL CONCEPT ANALYSIS; FORMAL CONCEPTS; FORMAL CONTEXTS; KNOWLEDGE DISCOVERY; MATHEMATICAL PROPERTIES; MATHEMATICAL THEORY; ONTOLOGY MERGING; THEORETICAL POINTS;

ALGEBRA; DATA REDUCTION; INFORMATION ANALYSIS; ONTOLOGY;

MERGING;

EID: 77957690417     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2010.08.020     Document Type: Article

References (42)

1. Ch. Aswani Kumar, and S. Srinivas Concept lattice reduction using fuzzy K-means clustering Expert Systems with Applications 37 2010 2696 2704
2. M. Bain Inductive construction of ontologies from formal concept analysis Australian Conference on Artificial Intelligence 2003 Springer Berlin 88 99
3. R. Belohlavek, Lattice generated by binary fuzzy relations (extended abstract), in: Fourth International Conference on Fuzzy Theory and Applications, 1998, p. 11.
4. R. Belohlavek Concept lattices and order in fuzzy logic Annals of Pure and Applied Logic 128 2004 277 298
5. R. Belohlavek Optimal triangular decompositions of matrices with entries from residuated lattices International Journal of Approximate Reasoning 50 2009 1250 1258
6. R. Belohlavek, and V. Vychodil Discovery of optimal factors in binary data via a novel method of matrix decomposition Journal of Computer and System Sciences 76 2009 3 20
7. R. Belohlavek, and V. Vychodil Formal concept analysis with background knowledge: attribute priorities IEEE Transactions on Systems, Man, and Cybernetics, Part C 39 2009 399 409
8. T. Berners-Lee The Semantic Web 2001 Scientific American
9. A. Burusco, and R. Fuentes-Gonzalez The study of L-fuzzy concept lattice Mathware & Soft Computing 3 1994 209 218
10. Y. Chen, and Y. Yao A multiview approach for intelligent data analysis based on data operators Information Sciences 178 2008 1 20
11. C. Carpineto, and G. Romano A lattice conceptual clustering system and its application to browsing retrieval Machine Learning 10 1996 95 122
12. J. Deogun, and J. Saquer Monotone concepts for formal concept analysis Discrete Applied Mathematics 144 2004 70 78
13. Y. Ding, D. Fensel, M. Klein, and B. Omelayenko The semantic web: yet another hip? Data and Knowledge Engineering 41 2-3 2002 205 227
14. P. du Boucher-Ryana, and D. Bridge Collaborative recommending using formal concept analysis Knowledge-Based Systems 19 2006 309 315
15. S. Fan, W. Zhang, and W. Xu Fuzzy inference based on fuzzy concept lattice Fuzzy Sets and Systems 157 2006 3177 3187
16. A. Formica Ontology-based concept similarity in formal concept analysis Information Sciences 176 2006 2624 2641
17. B. Ganter, and R. Wille Formal Concept Analysis: Mathematical Foundations 1999 Springer Berlin
18. G. Georgescu, and A. Popescu Concept lattices and similarity in non-commutative fuzzy logic Fundamenta Informaticae 55 2002 23 54
19. G. Georgescu, and A. Popescu Non-commutative fuzzy Galois connections Soft Computing 7 2003 458 467
20. Available from: .
21. S.O. Kuznetsov Machine learning and formal concept analysis P. Eklund, ICFCA 2004 Lecture Notes in Artificial Intelligence vol. 2961 2004 Springer-Verlag Berlin 287 312
22. H. Lai, and D. Zhang Concept lattices of fuzzy contexts: formal concept analysis vs. rough set theory International Journal of Approximate Reasoning 50 2009 695 707
23. M. Liu, M. Shao, W. Zhang, and C. Wu Reduction method for concept lattices based on rough set theory and its application Computers and Mathematics with Applications 53 2007 1390 1410
24. X. Liu, T. Chai, and W. Wang Approaches to the representations and logic operations for fuzzy concepts in the framework of axiomatic fuzzy set theory II Information Sciences 177 2007 1027 1045
25. X. Liu, and W. Pedrycz AFS Theory and It's Applications [M] 2009 Springer-Verlag Heidelberg
26. J. Medina, M. Ojeda-Aciego, A. Valverde, P. Vojtas, Towards biresiduated multi-adjoint logic programming, in: Lecture Notes in Artificial Intelligence, vol. 3040, 2004, pp. 608-617.
27. J. Medina, M. Ojeda-Aciego, J. Ruiz-Calvino, On multi-adjoint concept lattices: definition and representation theorem, in: Lecture Notes in Artificial Intelligence, vol. 4390, 2007, pp. 197-209.
28. J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calvino Relating generalized concept lattices and concept lattices for non-commutative conjunctors Applied Mathematics Letters 21 2008 1296 1300
29. G. Mineau, and R. Godin Automatic structuring of knowledge bases by conceptual clustering IEEE Transactions on Knowledge and Data Engineering 7 1995 824 829
30. N. Pasquier, Y. Bastide, R. Taouil, and L. Lakhal Efficient mining of association rules using closed itemset lattices Information Systems 24 1999 25 46
31. S. Pollandt Fuzzy Begriffe 1997 Springer Berlin
32. U. Priss Formal concept analysis in information science Annual Review of Information Science and Technology 40 2007 521 543
33. M. Ricordeau, and M. Liquiere Algebraic results and bottom-up algorithm for policies generalization in reinforcement learning using concept lattices Nonlinear Analysis: Hybrid Systems 2 2008 684 694
34. M. Shao, M. Liu, and W. Zhang Set approximations in fuzzy formal concept analysis Fuzzy Sets and Systems 158 2007 2627 2640
35. V. Snasel, M. Polovincak, H.M. Dahwa, Concept lattice reduction by singular value decomposition, in: Proceedings of the Spring Young Researcher's Colloquium on Database and Information Systems, Moscow, Russia, 2007, pp. 392-396.
36. G. Stumme, R. Taouil, Y. Bastide, N. Pasquier, and L. Lakhal Computing iceberg concept lattices with TITANIC Data and Knowledge Engineering 42 2002 189 222
37. H. Wang, and W. Zhang Approaches to knowledge reduction in generalized consistent decision formal context Mathematical and Computer Modelling 48 2008 1677 1684
38. L. Wang, and X. Liu Concept analysis via rough set and AFS algebra Information Sciences 178 2008 4125 4137
39. R. Wille Restructuring lattice theory: an approach based on hierarchies of concepts I. Rival, Ordered Sets 1982 Reidel 445 470
40. W. Wu, Y. Leung, and J. Mi Granular computing and knowledge reduction in formal contexts IEEE Transactions on Knowledge and Data Engineering 21 2009 1461 1474
41. Y. Yao, A comparative study of formal concept analysis and rough set theory in data analysis, in: Lecture Notes in Computer Science, LNAI 3066, 2004, pp. 59-68.
42. Y. Zhao, W.A. Halang, and X. Wang Rough ontology mapping in E-business integration Studies in Computational Intelligence 37 2007 75 93