What is a fuzzy concept lattice? II

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6743 LNAI, Issue , 2011, Pages 19-26

  Belohlavek, Radim ^a  

^a PALACKÝ UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

CONCEPT LATTICES; FOLLOW UP; FUZZY CONCEPT; FUZZY CONCEPT LATTICES;

FUZZY SETS; GRANULAR COMPUTING; ROUGH SET THEORY; DATA MINING;

INFORMATION ANALYSIS;

EID: 79960315287     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-21881-1_4     Document Type: Conference Paper

References (50)

1. Arnauld, A., Nicole, P.: La logique ou l'art de penser. English: Logic or the Art of Thinking, vol. 1662. Cambridge University Press, Cambridge (1996)
2. Bandler, W., Kohout, L.J.: Mathematical relations, their products and generalized morphisms. Technical Report EES-MMS-REL 77-3, ManMachine Systems Laboratory, Dept. Electrical Engineering, University of Essex, Essex, Colchester (1977)
3. Bandler, W., Kohout, L.J.: Semantics of implication operators and fuzzy relational products. Int. J. Man-Machine Studies 12, 89-116 (1980)
4. Barbut, M., Monjardet, B.: L'ordre et la classification, algèbre et combinatoire, tome II, Paris, Hachette (1970)
5. Belohlavek, R.: Lattices generated by binary fuzzy relations (extended abstract). In: Abstracts of FSTA 1998, Liptovský Ján, Slovakia, p. 11 (1998)
6. Belohlavek, R.: Fuzzy Galois connections. Math. Log. Quart. 45(4), 497-504 (1999)
7. Belohlavek, R.: Similarity relations in concept lattices. J. Logic Computation 10(6), 823-845 (2000)
8. Belohlavek, R.: Reduction and a simple proof of characterization of fuzzy concept lattices. Fundamenta Informaticae 46(4), 277-285 (2001)
9. Belohlavek, R.: Fuzzy closure operators. J. Mathematical Analysis and Applications 262, 473-489 (2001)
10. Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer Academic/Plenum Publishers, New York (2002)
11. Belohlavek, R.: Concept lattices and order in fuzzy logic. Annals of Pure and Applied Logic 128, 277-298 (2004)
12. Belohlavek, R.: Sup-t-norm and inf-residuum are one type of relational product: unifying framework and consequences. Fuzzy Sets and Systems (to appear)
13. Belohlavek, R.: Reduction of formal contexts as computing base: the case of binary and fuzzy attributes (to be submitted)
14. Belohlavek, R., De Baets, B., Outrata, J., Vychodil, V.: Computing the lattice of all fixpoints of a fuzzy closure operator. IEEE Transactions on Fuzzy Systems 18(3), 546-557 (2010)
15. Belohlavek, R., Dvorak, J., Outrata, J.: Fast factorization by similarity in formal concept analysis of data with fuzzy attributes. J. Computer and System Sciences 73(6), 1012-1022 (2007)
16. Bělohlávek, R., Sklenář, V., Zacpal, J.: Crisply generated fuzzy concepts. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 269-284. Springer, Heidelberg (2005)
17. Belohlavek, R., Vychodil, V.: Reducing the size of fuzzy concept lattices by hedges. In: Proc. FUZZ-IEEE 2005, Reno, Nevada, pp. 663-668 (2005)
18. Belohlavek, R., Vychodil, V.: What is a fuzzy concept lattice? In: Proc. CLA 2005. CEUR WS, vol. 162, pp. 34-45 (2005)
19. Bělohlávek, R., Vychodil, V.: Attribute implications in a fuzzy setting. In: Missaoui, R., Schmidt, J. (eds.) Formal Concept Analysis. LNCS (LNAI), vol. 3874, pp. 45-60. Springer, Heidelberg (2006)
20. Belohlavek, R., Vychodil, V.: Factor Analysis of Incidence Data via Novel Decomposition of Matrices. In: Ferré, S., Rudolph, S. (eds.) ICFCA 2009. LNCS, vol. 5548, pp. 83-97. Springer, Heidelberg (2009)
21. Ben Yahia, S., Jaoua, A.: Discovering knowledge from fuzzy concept lattice. In: Kandel, A., Last, M., Bunke, H. (eds.) Data Mining and Computational Intelligence, pp. 167-190. Physica-Verlag, Heidelberg (2001)
22. Burusco, A., Fuentes-Gonzáles, R.: The study of the L-fuzzy concept lattice. Mathware & Soft Computing 3, 209-218 (1994)
23. Burusco, A., Fuentes-Gonzáles, R.: Concept lattice defined from implication operators. Fuzzy Sets and Systems 114(3), 431-436 (2000)
24. Ganter, B., Kuznetsov, S.O.: Pattern structures and their projections. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 129-142. Springer, Heidelberg (2001)
25. Ganter, B., Wille, R.: Formal Concept Analysis. Mathematical Foundations. Springer, Berlin (1999)
26. Gediga G., Düntsch I.: Modal-style operators in qualitative data analysis. In: Proc. IEEE ICDM 2002, p. 155 (Technical Report # CS-02-15, Brock University, 15 pp.) (2002)
27. Gély, A., Medina, R., Nourine, L.: Representing lattices using many-valued relations. Information Sciences 179(16), 2729-2739 (2009)
28. Georgescu, G., Popescu, A.: Concept lattices and similarity in non-commutative fuzzy logic. Fundamenta Informaticae 53(1), 23-54 (2002)
29. Georgescu, G., Popescu, A.: Non-dual fuzzy connections. Archive for Mathematical Logic 43, 1009-1039 (2004)
30. Goguen, J.A.: The logic of inexact concepts. Synthese 18, 325-373 (1968-1969)
31. Gottwald, S.: A Treatise on Many-Valued Logics. Research Studies Press, Baldock (2001)
32. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)
33. Heider, E.R.: Universals in color naming and memory. J. of Experimental Psychology 93, 10-20 (1972)
34. Höhle, U.: On the fundamentals of fuzzy set theory. J. Mathematical Analysis and Applications 201, 786-826 (1996)
35. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice-Hall, Englewood Cliffs (1995)
36. Krajči, S.: Cluster based efficient generation of fuzzy concepts. Neural Network World 5, 521-530 (2003)
37. Krajči, S.: The basic theorem on generalized concept lattice. In: Bělohlávek, R., Snášel, V. (eds.) Proc. of 2nd Int.Workshop on CLA 2004, Ostrava, pp. 25-33 (2004)
38. Krajči, S.: A generalized concept lattice. Logic J. of IGPL 13, 543-550 (2005)
39. Krajči, S.: Every concept lattice with hedges is isomorphic to some generalized concept lattice. In: Proc. CLA 2005. CEUR WS, vol. 162, pp. 1-9 (2005)
40. Krupka, M.: Main theorem of fuzzy concept lattices revisited (submitted)
41. Lai, H., Zhang, D.: Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory. Int. J. Approximate Reasoning 50(5), 695-707 (2009)
42. Medina, J., Ojeda-Aciego, M., Ruiz-Claviño, J.: Formal concept analysis via multi-adjoint concept lattices. Fuzzy Sets and Systems 160, 130-144 (2009)
43. Miller, G.A.: The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review 63(2), 343-355 (1956)
44. Pankratieva, V.V., Kuznetsov, S.O.: Relations between proto-fuzzy concepts, crisply generated fuzzy concepts, and interval pattern structures. In: Proc. CLA 2010. CEUR WS, vol. 672, pp. 50-59 (2010)
45. Pollandt, S.: Fuzzy Begriffe. Springer, Berlin (1997)
46. Rosch, E.: Natural categories. Cognitive Psychology 4, 328-350 (1973)
47. Ward, M., Dilworth, R.P.: Residuated lattices. Trans. AMS 45, 335-354 (1939)
48. Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445-470. Reidel, Dordrecht (1982)
49. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338-353 (1965)
50. Zhao, H., Zhang, D.: Many vaued lattice and their representations. Fuzzy Sets and Sytems 159, 81-94 (2008)