On the definition of suitable orderings to generate adjunctions over an unstructured codomain

Information Sciences

Volumn 286, Issue , 2014, Pages 173-187

  Garcia Pardo F ^a   Cabrera, I P ^a   Cordero, P ^a   Ojeda Aciego, M ^a   Rodriguez F J ^a  

^a UNIVERSITY OF MÁLAGA   (Spain)

Author keywords

Adjunction; Isotone Galois connection; Partial order relation; Preorder relation

Indexed keywords

SET THEORY;

ADJUNCTIONS; CLOSURE OPERATORS; CLOSURE SYSTEMS; GALOIS CONNECTION; ORDER RELATION; ORDERED SET; PARTIAL ORDER RELATION; PREORDER RELATION;

MAPPING;

EID: 84906712556     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2014.07.006     Document Type: Article

References (44)

1. L. Antoni, S. Krajči, O. Krídlo, B. Macek, and L. Pisková On heterogeneous formal contexts Fuzzy Sets Syst. 234 2014 22 33
2. H.G. Bartel Formal concept analysis and chemometrics: chemical composition of ancient egyptian bronze artifacts MATCH Commun. Math. Comput. Chem. 42 2000 25 38
3. R. Bělohlávek Fuzzy Galois connections Math. Logic Quart. 45 4 1999 497 504
4. R. Bělohlávek, P.Osička, Triadic fuzzy Galois connections as ordinary connections, in: I. Press, (Ed.), IEEE Intl Conf on Fuzzy Systems, 2012.
5. R. Belohlávek, and J. Konecny Concept lattices of isotone vs. antitone Galois connections in graded setting: mutual reducibility revisited Inform. Sci. 199 2012 133 137
6. P. Butka, J. Pócs, and J. Pócsová On equivalence of conceptual scaling and generalized one-sided concept lattices Inform. Sci. 259 2014 57 70
7. I.P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego A coalgebraic approach to non-determinism: applications to multilattices Inform. Sci. 180 22 2010 4323 4335
8. I.P. Cabrera, P. Cordero, G. Gutiérrez, J. Martínez, and M. Ojeda-Aciego Finitary coalgebraic multisemilattices and multilattices Appl. Math. Comput. 219 1 2012 31 44
9. G. Castellini, J. Koslowski, and G. Strecker Closure operators and polarities Ann. NY Acad. Sci. 704 1993
10. D. Cohen, P.J.P. Creed, and S. Živný An algebraic theory of complexity for valued constraints: establishing a Galois connection Lect. Notes Comput. Sci. 6907 2011 231 242
11. K. Denecke, M. Erné, and S. Wismath Galois Connections and Applications Mathematics and its Applications vol. 565 2004 Springer
12. J. Díaz, and J. Medina Multi-adjoint relation equations: definition, properties and solutions using concept lattices Inform. Sci. 253 2013 100 109
13. D. Dubois, and H. Prade Possibility theory and formal concept analysis: characterizing independent sub-contexts Fuzzy Sets Syst. 196 2012 4 16
14. W. Dzik, J. Järvinen, and M. Kondo Intuitionistic propositional logic with Galois connections Logic J. IGPL 18 6 2010 837 858
15. W. Dzik, J. Järvinen, and M. Kondo Representing expansions of bounded distributive lattices with Galois connections in terms of rough sets Int. J. Approx. Reason. 55 1 2014 427 435
16. M. Erné, J. Koslowski, A. Melton, and G. Strecker A primer on Galois connections Ann. NY Acad. Sci. 704 1993 103 125
17. F. Fages, and S. Soliman Abstract interpretation and types for systems biology Theor. Comput. Sci. 403 1 2008 52 70
18. S. Ferré, and R. King BLID: an application of logical information systems to bioinformatics Lect. Notes Comput. Sci. 2961 2004 47 54
19. A. Frascella Fuzzy Galois connections under weak conditions Fuzzy Sets Syst. 172 1 2011 33 50
20. B. Galitsky, B. Kovalerchuk, and S. Kuznetsov Learning common outcomes of communicative actions represented by labeled graphs Lect. Notes Comput. Sci. 4604 2007 387 400
21. B. Ganter, and S. Kuznetsov Pattern structures and their projections Lect. Notes Comput. Sci. 2120 2001 129 142
22. F. García-Pardo, I.P. Cabrera, P. Cordero, and M. Ojeda-Aciego On Galois connections and soft computing Lect. Notes Comput. Sci. 7903 2013 224 235
23. L. Guo, G.-Q. Zhang, and Q. Li Fuzzy closure systems on L-ordered sets Math. Logic Quart. 57 3 2011 281 291
24. J. Järvinen Pawlak's information systems in terms of Galois connections and functional dependencies Fundam. Inform. 75 2007 315 330
25. J. Järvinen, M. Kondo, and J. Kortelainen Logics from Galois connections Int. J. Approx. Reason. 49 3 2008 595 606
26. D.M. Kan Adjoint functors Trans. Am. Math. Soc. 87 2 1958 294 329
27. A. Kerber Posets and lattices, contexts and concepts MATCH Commun. Math. Comput. Chem. 54 2005 551 560
28. S. Kerkhoff A general Galois theory for operations and relations in arbitrary categories Algebra Univ. 68 3 2012 325 352
29. J. Konecny Isotone fuzzy Galois connections with hedges Inform. Sci. 181 10 2011 1804 1817
30. S. Kuznetsov Fitting pattern structures to knowledge discovery in big data Lect. Notes Comput. Sci. 7880 2013 254 266
31. J. Lambek Iterated Galois connections in arithmetic and linguistics K. Denecke, M. Erné, S. Wismath, Galois Connections and Applications Mathematics and Its Applications vol. 565 2004 Springer Netherlands 389 397
32. A.N.M. Kaytoue, S.O. Kuznetsov, and S. Duplessis Mining gene expression data with pattern structures in formal concept analysis Inform. Sci. 181 10 2011 1989 2001
33. J. Medina Multi-adjoint property-oriented and object-oriented concept lattices Inform. Sci. 190 2012 95 106
34. J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño Formal concept analysis via multi-adjoint concept lattices Fuzzy Sets Syst. 160 2 2009 130 144
35. J. Medina, M. Ojeda-Aciego, and J. Ruiz-Calviño Concept-forming operators on multilattices Lect. Notes in Comput. Sci. 7880 2013 203 215
36. A. Melton, D. Schmidt, and G.E. Strecker Galois connections and computer science applications Lect. Notes Comput. Sci. 240 1986 299 312
37. M. Moortgat Multimodal linguistic inference J. Logic, Lang. Inform. 5 3-4 1996 349 385
38. S.-C. Mu, and J.N. Oliveira Programming from Galois connections J. Logic Algebr. Programm. 81 6 2012 680 704
39. O. Ore Galois connections Trans. Am. Math. Soc. 55 1944 493 513
40. M. Restrepo, C. Cornelis, and J. Gómez Duality, conjugacy and adjointness of approximation operators in covering-based rough sets Int. J. Approx. Reason. 55 1 2014 469 485
41. F. Rioult, J.-F. Boulicaut, B. Crémilleux, and J. Besson Using transposition for pattern discovery from microarray data Proceedings of the 8th ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery DMKD '03 2003 Springer New York, NY, USA 73 79
42. F.J. Valverde-Albacete, and C. Peláez-Moreno Extending conceptualisation modes for generalised formal concept analysis Inform. Sci. 181 10 2011 1888 1909
43. K. Wang, and B. Zhao Join-completions of L-ordered sets Fuzzy Sets Syst. 199 2012 92 107
44. W. Yao, and B. Zhao Kernel systems on L-ordered sets Fuzzy Sets Syst. 182 1 2011 101 109