The Dedekind-MacNeille completions for fuzzy posets

Fuzzy Sets and Systems

Volumn 160, Issue 16, 2009, Pages 2292-2316

  Xie, Weixian ^a   Zhang, Qiye ^b,c   Fan, Lei ^d  

^a BEIJING INSTITUTE OF FASHION TECHNOLOGY   (China)

^b BEIHANG UNIVERSITY   (China)

^c BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

^d CAPITAL NORMAL UNIVERSITY   (China)

Author keywords

Completely lattice L ordered set; Dedekind MacNeille completion; Fuzzy order; L concept lattice; L fuzzy complete lattice; L fuzzy poset

Indexed keywords

COMPLETELY LATTICE L-ORDERED SET; DEDEKIND-MACNEILLE COMPLETION; FUZZY ORDER; L-CONCEPT LATTICE; L-FUZZY COMPLETE LATTICE; L-FUZZY POSET;

SET THEORY;

EID: 67349118109     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2008.12.002     Document Type: Article

References (18)

1. Bělohlávek R. Fuzzy Relational Systems, Foundations and Principles (2002), Kluwer Academic, Plenum Publishers, New York
2. Bělohlávek R. Concept lattices and order in fuzzy logic. Annals of Pure and Applied Logic 128 (2004) 277-298
3. Bělohlávek R. Lattice-type fuzzy order is uniquely given by its 1-cut: proof and consequences. Fuzzy Sets and Systems 123 (2004) 447-458
4. Davey B.A., and Priestley H.A. Introduction to Lattices and Order (1990), Cambridge University Press, Cambridge
5. Fan L. A new approach to quantitative domain theory. Electronic Notes in Theoretic Computer Science 45 (2001). http://www.elsevier.nl/locate/entcs 〈http://www.elsevier.nl/locate/entcs〉
6. Gierz G., Hofmann K.H., Keimel K., Lawson J.D., Mislove M., and Scott D.S. A Compendium of Continuous Lattices (1980), Springer, Berlin, Heidelberg, New York
7. Goguen J.A. L-fuzzy sets. Journal of Mathematical Analysis and Application 18 (1967) 145-174
8. Höhle U. On the fundamentals of fuzzy set theory. Journal of Mathematical Analysis and Application 201 (1996) 786-826
9. U. Höhle, M-valued sets and sheaves over integral commutative cl-Monoids, Chapter 2 in [13], pp. 33-72.
10. Höhle U., and Blanchard N. Partial ordering in L-underdeterminate sets. Information Science 35 (1985) 133-144
11. H.L. Lai, D.X. Zhang, Many-valued complete distributivity, arXiv:math.CT/0603590, 2006.
12. Johnstone P.T. Stone Spaces (1982), Cambridge University Press, Cambridge
13. S.E. Rodabaugh, E.P. Klement, U. Höhle (Eds.), Applications of Category Theory to Fuzzy Subsets, Theory and Decision Library: Series B: Mathematical and Statistical Methods, Vol. 14, 1992, Kluwer Academic Publishers, Boston, Dordrecht, London.
14. K.R. Wagner, Solving recursive domain equations with enriched categories, Ph.D. Thesis, Carnegie Mellon University, Technical Report CMU-CS-94-159, July 1994.
15. Zhang Q.Y., and Fan L. Continuity in quantitative domains. Fuzzy Sets and Systems 154 (2005) 118-131
16. Zhang Q.Y., and Fan L. A kind of L-fuzzy complete lattices and adjoint functor theorem for LF-posets. Report on the Fourth International Symposium on Domain Theory (June 2006), Hunan University, Changsha, China
17. Q.Y. Zhang, W.X. Xie, L. Fan, Fuzzy complete lattices, Fuzzy Sets and Systems, in press, doi:10.1016/j.fss.2008.12.001.
18. Q.Y. Zhang, L. Fan, W.X. Xie, Adjoint functor theorem for fuzzy posets, Bulletin of the Allahabad Mathematical Society, submitted for publication.