Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued "intuitionistic" sets, "intuitionistic" fuzzy sets and topologies

Fuzzy Sets and Systems

Volumn 156, Issue 3, 2005, Pages 445-484

  Gutierrez Garcia J ^a   Rodabaugh, S E ^b  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^b YOUNGSTOWN STATE UNIVERSITY   (United States)

Author keywords

Categorical (functorial) isomorphism; DeMorgan algebras; L double double fuzzy topology; L double fuzzy topology; L double gradation fuzzy topology; L double topology; L fuzzy topology; L topology; Order isomorphism; Semi DeMorgan algebras; Semi polarity

Indexed keywords

ALGEBRA; SET THEORY; TOPOLOGY;

FUZZY TOPOLOGY; L-DOUBLE TOPOLOGY; L-TOPOLOGY; ORDER-ISOMORPHISM;

FUZZY SETS;

EID: 26944486863     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2005.05.023     Document Type: Article

References (54)

1. S.E. Abbas Intuitionistic supra fuzzy topological spaces Chaos, Solitons & Fractals 21 5 2004 1205 1214
2. J. Adámek, H. Herrlich, and G.E. Strecker Abstract and Concrete Categories: The Joy Of Cats, Wiley Interscience Pure and Applied Mathematics 1990 Wiley Brisbane/Chichester/New York/Singapore/Toronto
3. K.T. Atanassov Intuitionistic fuzzy sets V. Sgurev VII ITKR's session (Sofia, June 1983), Central Science and Technology Library 1984 Bulgarian Academy of Sciences
4. K.T. Atanassov Intuitionistic fuzzy sets Fuzzy Sets and Systems 20 1986 87 96
5. K.T. Atanassov Intutionistic Fuzzy Sets 1999 Physica-Verlag Heidelberg/New York
6. K. Atanassov, and G. Gargov Interval-valued intuitionistic fuzzy sets Fuzzy Sets and Systems 31 1989 343 349
7. K.T. Atanassov, S. Stoeva, Intuitionistic L-fuzzy sets, in: Polish Symposium on Interval and Fuzzy Mathematics, Poznań, August 1983, pp. 23-26.
8. B. Banaschewski, and C.J. Mulvey A constructive proof of the Stone-Weierstrass theorem J. Pure Appl. Algebra 116 1977 25 40
9. M. Barr Toposes without points J. Pure and Appl. Algebra 5 1974 265 280
10. G.D. Birkhoff Lattice Theory, American Mathematical Society, Colloq. Publ. XXXV third ed. 1967 AMS Providence, RI
11. E.A. Bishop Foundations of Constructive Analysis 1967 McGraw-Hill New York
12. D.S. Bridges Constructive Functional Analysis 1979 Pitman London
13. C.W. Burden The Hahn-Banach Theorem in a category of sheaves J. Pure Appl. Algebra 17 1980 25 34
14. H. Bustince, and P. Burillo Vague sets are intuitionistic fuzzy sets Fuzzy Sets and Systems 79 1996 403 405
15. C.L. Chang Fuzzy topology J. Math. Anal. Appl. 24 1968 182 190
16. R. Cignoli, F. Esteva, L. Godo, and F. Montagna On a class of left-continuous t -norms Fuzzy Sets and Systems 131 3 2002 283 296
17. D. Çoker An introduction to intuitionistic fuzzy topological spaces Fuzzy Sets and Systems 88 1997 81 89
18. D. Çoker, and M. Demirci An introduction to intuitionistic fuzzy topological spaces in Šostak's sense Busefal 67 1996 67 76
19. J.L. Deng Introduction to grey system theory J. Grey Systems 1 1989 1 24
20. J.L. Deng Grey information space J. Grey Systems 1 1989 103 117
21. G. Deschrijver, and E.E. Kerre On the relationship between some extensions of fuzzy set theory Fuzzy Sets and Systems 133 2004 227 235
22. D. Dubois, S. Gottwald, P. Hájek, J. Kacpryzk, H. Prade, Are "intuitionistic" fuzzy sets intuitionistic? Fuzzy Sets and Systems, to appear.
23. F. Esteva, L. Godo, P. Hájek, and M. Navara Residuated fuzzy logics with an involutive negation Archive for Math. Logic 39 2 2000 103 124
24. G.M. French, Syntactic and semantic aspects of locales and quantales, Thesis, University of Sussex, 1992.
25. W.L. Gau, and D.J. Buehrer Vague sets IEEE Trans. Systems Man Cybernet. 23 2 1993 610 614
26. J.A. Goguen The fuzzy Tychonoff Theorem J. Math. Anal. Appl. 43 1973 734 742
27. E. Hewitt, and K. Stromberg Real and Abstract Analysis 1965 Springer Berlin/Heidelberg/New York
28. U. Höhle Upper semicontinuous fuzzy sets and applications J. Math. Anal. Appl. 78 1980 659 673
29. 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.
30. U. Höhle, A. Šostak, Axiomatic foundations of fixed-basis fuzzy topology, Chapter 3 in [29], pp. 123-272.
31. P.T. Johnstone Topos Theory 1977 Academic Press London
32. P.T. Johnstone Tychonoff's theorem without the axiom of choice Fund. Math. 113 1981 21 35
33. P.T. Johnstone Stone Spaces 1982 Cambridge University Press Cambridge
34. W. Kotzé (Ed.), Special Issue, Quaestiones Mathematicae 20 (3) (1997).
35. W.J. Kotzé, Lifting of sobriety concepts with particular reference to (L, M ) -topological spaces, Chapter 16 in [47], pp. 415-426.
36. T. Kubiak On Fuzzy topologies, Doctoral Dissertation 1985 Adam Mickiewicz University Poznań, Poland
37. T. Kubiak, A.P. Šostak, Lower set-valued fuzzy topologies, in [34], pp. 423-429.
38. S.J. Lee, and E.P. Lee The category of intuitionistic fuzzy topological spaces Bulletin Korean Math. Soc. 37 2000 63 76
39. T.K. Mondal, and S.K. Samanta On intuitionistic gradation of openness Fuzzy Sets and Systems 131 2002 323 336
40. C.J. Mulvey Intuitionistic algebra and representation of rings Memoirs Amer. Math. Soc. 148 1974 3 57
41. C.J. Mulvey, J.W. Pelletier, On the points of locales in a De Morgan topos, in: Categorical Topology, Toledo, 1983, Sigma Ser. in Pure Math. 5 (1984) 392-407, Heldermann.
42. C.J. Mulvey, Geometry of choice, Chapter 11 in [47], pp. 309-336.
43. S.E. Rodabaugh Point-set lattice-theoretic topology Fuzzy Sets and Systems 40 1991 297 345
44. S.E. Rodabaugh, Powerset operator based foundation for point-set lattice-theoretic (poslat) fuzzy set theories and topologies, in [34], pp. 463-530.
45. S.E. Rodabaugh, Powerset operator foundations for poslat fuzzy set theories and topologies, Chapter 2 in [29], pp. 91-116.
46. S.E. Rodabaugh, Categorical foundations of variable-basis fuzzy topology, Chapter 4 in [29], pp. 273-388.
47. S.E. Rodabaugh, E.P. Klement (Eds.), Topological and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic, vol. 20, Kluwer Academic Publishers Boston/Dordrecht/ London, 2003.
48. S.K. Samanta, and T.K. Mondal Intuitionistic gradation of openness: intuitionistic fuzzy topology Busefal 73 1997 8 17
49. A.P. Šostak On a fuzzy topological structure Suppl. Rend. Circ. Matem. Palermo, sr. II 11 1985 89 103
50. J. Staples On constructive fields Proc. London Math. Soc. 23 1971 753 768
51. J.J.C. Vermeulen, Constructive techniques in functional analysis, Dissertation, University of Sussex, 1986.
52. S. Vickers, Topology Via Logic, Cambridge Tracts in Theoretical Computer Science, vol. 5, reprinted 1990, paperback 1996, Cambridge University Press, Cambridge/Melbourne/New York, 1989.
53. G.-J. Wang, and Y.-Y. He Intuitionistic fuzzy sets and L -fuzzy sets Fuzzy Sets and Systems 110 2000 271 274
54. L. Zadeh The concept of a linguistic variable and its application to approximate reasoning - I Inform. Sci. 8 1975 199 249