I-fuzzy Alexandrov topologies and specialization orders

Fuzzy Sets and Systems

Volumn 158, Issue 21, 2007, Pages 2359-2374

  Jinming, Fang ^a  

^a OCEAN UNIVERSITY OF CHINA   (China)

Author keywords

Alexandrov topology; Fuzzy preorder; I fuzzy topology; Specialization order; Triangular norm

Indexed keywords

FORMAL LOGIC; THEOREM PROVING; TOPOLOGY;

ALEXANDROV TOPOLOGY; FUZZY PREORDERS; FUZZY TOPOLOGY; SPECIALIZATION ORDERS;

FUZZY SETS;

EID: 34548175385     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2007.05.001     Document Type: Article

References (24)

1. Adamek J., Herrlich H., and Strecker G.E. Abstract and Concrete Categories (1990), Wiley, New York
2. Bodenhofer U., De Baets B., and Fodor J. A compendium of fuzzy weak orders: representations and characterizations. Fuzzy Sets and Systems 158 (2007) 811-829
3. Bodenhofer U., De Cock M., and Kerre E.E. Openings and closures of fuzzy orderings: theoretical basis and applications to fuzzy rule-based systems. Internat. J. Gen. Systems 32 (2003) 343-360
4. J.M. Fang, P.W. Chen, One-to-one correspondence between fuzzifying topologies and fuzzy preorders, Fuzzy Sets and Systems, accepted for publication.
5. Höhle U. Upper semicontinuous fuzzy sets and applications. J. Math. Anal. Appl. 78 (1980) 659-673
6. U. Höhle, S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series, Vol. 3, Kluwer Academic Publishers, Boston, Dordrecht, London, 1999.
7. Höhle U., and Šostak A. Axiomatic foundations of variable-basis fuzzy topology. In: Höhle U., and Rodabaugh S.E. (Eds). Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series, Vol. 3 (1999), Kluwer Academic Publishers, Boston, Dordrecht, London 123-272
8. Jacas J., and Recasens J. Fixed points and generators of fuzzy relations. J. Math. Anal. Appl. 186 (1994) 21-29
9. Jacas J., and Recasens J. Fuzzy T-transitive relations: eigenvectors and generators. Fuzzy Sets and Systems 72 (1995) 147-154
10. Kelley J.L. General Topology, Graduate Text in Mathematics Vol. 27 (1975), Springer, Berlin
11. Klawonn F., and Castro J.L. Similarity in fuzzy reasoning. Math. Soft. Comput. 2 (1995) 197-228
12. Klement E.P., Mesiar R., and Pap E. Triangular norms. Trends in Logic Vol. 8 (2000), Kluwer Academic Publishers, Dordrecht
13. J. Kortelainen, Some compositional modifier operators generate L-interior operators, in: Proceedings of 10th IFSA World Congress, 2003, pp. 480-483.
14. T. Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, 1985.
15. Lai H., and Zhang D. Fuzzy preorder and fuzzy topology. Fuzzy Sets and Systems 157 (2006) 1865-1885
16. Lowen R. Fuzzy topological spaces and fuzzy compactness. J. Math. Anal. Appl. 56 (1976) 623-633
17. Lowen R. Initial and final fuzzy topologies and the fuzzy Tychonoff theorem. J. Math. Anal. Appl. 58 (1977) 11-21
18. Qin K., and Pei Z. On the topological properties of fuzzy rough sets. Fuzzy Sets and Systems 151 (2005) 605-613
19. Rodabaugh S.E. Categorical foundations of variable-basis fuzzy topology. In: Höhle U., and Rodabaugh S.E. (Eds). Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series Vol. 3 (1999), Kluwer Academic Publishers, Boston, Dordrecht, London 273-388
20. Schweizer B., and Sklar A. Probabilistic Metric Spaces (1983), North-Holland, Amsterdam
21. Šostak A. Two decades of fuzzy topology: basic ideas notions and results. Russian Math. Surveys 44 (1989) 125-186
22. Valverde L. On the structure of F-indistinguishability operators. Fuzzy Sets and Systems 17 (1985) 313-328
23. Ying M.S. A new approach to fuzzy topology (I). Fuzzy Sets and Systems 39 3 (1991) 303-321
24. Zhang D.X. L-Fuzzifying topologies as L-topologies. Fuzzy Sets and Systems 125 (2002) 135-144