Topological properties of the class of generators of an indistinguishability operator

Fuzzy Sets and Systems

Volumn 143, Issue 3, 2004, Pages 413-426

  Demirci, Mustafa ^a  

^a AKDENIZ UNIVERSITY   (Turkey)

Author keywords

Fuzzy equality; Fuzzy topology; Indistinguishability operator; Metrizability; Pseudo metrizability; Topology

Indexed keywords

FUNCTIONS; FUZZY SETS; THEOREM PROVING; TOPOLOGY;

FUZZY EQUALITY; FUZZY TOPOLOGY; INDISTINGUISHABILITY OPERATOR; METRIZABILITY; PSEUDO-METRIZABILITY;

MATHEMATICAL OPERATORS;

EID: 1842527717     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(03)00181-7     Document Type: Article

References (28)

1. Bezdek J.C., Harris J.O. Fuzzy partitions and relations. an axiomatic basis for clustering Fuzzy Sets and Systems. 1:1978;112-127.
2. Bodenhofer U. A similarity-based generalization of fuzzy orderings preserving the classical axioms. Internat. J. Uncertainty Fuzziness Knowledge-Based Systems. 8(5):2000;593-610.
3. Boixader D., Jacas J., Recasens J. Fuzzy equivalence relations: advanced material. Dubois D., Prade H. Fundamentals of Fuzzy Sets. 2000;261-290 Kluwer Academic Publishers, Boston.
4. Boixader D., Jacas J., Recasens J. Upper and lower approximations of fuzzy sets. Internat. J. General Systems. 29:2000;555-568.
5. Chang C.L. Fuzzy topological spaces. J. Math. Anal. Appl. 24:1968;182-190.
6. De Baets B., Mesiar R. Pseudo-metrics and. script T sign-equivalences J. Fuzzy Math. 5:1997;471-481.
7. De Baets B., Mesiar R. Metrics and. script T sign-equalities J. Math. Anal. Appl. 267:2002;531-547.
8. Demirci M. Fuzzy functions and their applications. J. Math. Anal. Appl. 252:2000;495-517.
9. Höhle U. Quotients with respect to similarity relations. Fuzzy Sets and Systems. 27:1988;31-44.
10. U. Höhle, Commutative, residuated l-monoids, in: U. Höhle, E.P. Klement (Eds.), Non-Classical Logics and Their Applications to Fuzzy Subsets, vol. 32, Kluwer Academic Publishers, Dordrecht, 1995, pp. 53-106.
11. Höhle U. Classification of subsheaves over GL-algebra. Buss S.R., Hajek P., Pudlak P. Logic Colloquium'98. Lecture Notes in Logic. vol. 13:1998;238-261 Springer, Berlin.
12. Höhle U., Šostak A.P. A general theory of fuzzy topological spaces. Fuzzy Sets and Systems. 73:1995;131-149.
13. Höhle U., Šostak A.P. Axiomatic foundations of fixed-basis fuzzy topology. Höhle U., Rodabaugh S.E. Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory. 1999;123-272 Kluwer Academic Publishers, Boston.
14. Jacas J. Fuzzy topologies induced by S-metrics. J. Fuzzy Math. 1:1993;173-191.
15. Jacas J., Recasens J. Fixed points and generators of fuzzy relations. J. Math. Anal. Appl. 186:1994;21-29.
16. Jacas J., Recasens J. Fuzzy T-transitive relations. eigenvectors and generators Fuzzy Sets and Systems. 72:1995;147-154.
17. Klawonn F., Castro J.L. Similarity in fuzzy reasoning. Mathware Soft Comput. 2:1995;197-228.
18. Klement E.P., Mesiar R., Pap E. Triangular norms. Trends in Logic. vol. 8:2000;Kluwer Academic Publishers, Dordrecht.
19. Ling C. Representation of associative functions. Publ. Math. Debrecen. 12:1965;189-212.
20. Lowen R. Fuzzy topological spaces and fuzzy compactness. J. Math. Anal. Appl. 56:1976;621-633.
21. Lowen R. A comparison of different compactness notions in fuzzy topological spaces. J. Math. Anal. Appl. 64:1978;446-454.
22. Menger K. Probabilistic theory of relations. Proc. Nat. Acad. Sci. USA. 37:1951;178-180.
23. Nagata J. Modern General Topology. 1974;North-Holland Publishing Company, Amsterdam.
24. Novak V. Fuzzy Sets and their Applications. 1986;Adam Hilger, Bristol.
25. E. Trillas, Sobre functions de negación en la teoria de conjuntos disfusos, Stochastica 3 (1979) 47-60 (in Spanish). Reprinted (English Version) in: S. Barro, et al. (Eds.), Advances of Fuzzy Logic, Universidad de Santiago de Compostela, 1998, pp. 31-43.
26. E. Trillas, Sobre functions de negación en la teoria de conjuntos disfusos, Stochastica 3 (1979) 47-60 (in Spanish). Reprinted (English Version) in: S. Barro, et al. (Eds.), Advances of Fuzzy Logic, Universidad de Santiago de Compostela, 1998, pp. 31-43.
27. Valverde L. On the structure of F-indistinguishability operators. Fuzzy Sets and Systems. 17:1985;313-328.
28. Zadeh L.A. Similarity relations and fuzzy orderings. Inform. Sci. 3:1971;177-200.