호남수학학술지 (Honam Mathematical Journal)

  • 제32권2호
  • /
  • Pages.333-362
  • /
  • 2010
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

H * H-FUZZY SETS

  • Lee, Wang-Ro (Faculty of Liberal Education, Chonbuk National University) ;
  • Hur, Kul (Division of Mathematics and Informational Statistics Wonkwang University)
  • 투고 : 2009.10.13
  • 심사 : 2010.05.27
  • 발행 : 2010.06.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We define H*H-fuzzy set and form a new category Set(H*H) consisting of H*H-fuzzy sets and morphisms between them. First, we study it in the sense of topological universe and obtain an exponential objects of Set(H*H). Second, we investigate some relationships among the categories Set(H*H), Set(H) and ISet(H).

키워드

참고문헌

  1. J. Adamek and H. Herrlich, Cartrsian closed categories, quasitopi and topological Universe, Comment. Math. Univ. Carolin. 27 (2) (1986), 235-257.
  2. G. Birkhoff, Lattice Theory (A.M.S. Colloquium Publication Vol XXV, 1967).
  3. K. A. Dib and Nabil L. Youssef, Fuzzy cartesian product, fuzzy relations and fuzzy functions, Fuzzy Sets and Systems 41 (1991), 299-315. https://doi.org/10.1016/0165-0114(91)90134-C
  4. J. C. Carrega, The category Rel(H) and Fuz(H), Fuzzy Sets and Systems 9 (1983), 327-332. https://doi.org/10.1016/S0165-0114(83)80031-1
  5. E. J. Dubuc, Concrete quasitopoi, Applications of Sheaves. Proc. Dunham 1977, Lect. Notes in Math. 753 (1979), 239-254. https://doi.org/10.1007/BFb0061821
  6. E. Eytan, Fuzzy sets: a topological point of view, Fuzzy Sets and Systems 5 (1981), 47-67. https://doi.org/10.1016/0165-0114(81)90033-6
  7. J. A. Goguen, Categories of V-sets, Bull. Amer. Math. Soc. 75 (1969), 622-624. https://doi.org/10.1090/S0002-9904-1969-12267-6
  8. H. Herrlich, Cartesian closed topological categories, Math. Coll. Univ. Cape Town 9 (1974), 1-16.
  9. H. Herrlich and G. E. Strecker, Category Theory (Allyn and Bacon, Newton, MA, 1973).
  10. K. Hur, A note on the category Set(H), Honam Math. J. 10 (1988), 89-94.
  11. K. Hur, H. W. Kang and J. H. Ryou, Intuitionistic H-fuzzy sets, J. Korea Soc. Math. Educ. Ser. B; Pure Appl. Math. 12 (1) (2005), 33-45.
  12. P. T. Johnstone, Stone spaces, Cambridge University Press (1982).
  13. C. Y. Kim, S. S. Hong, Y. H. Hong and P. H. Park, Algebras in Cartesian closed topological categories, Lecture Note Series 1, 26 (1985).
  14. C. V. Negoita and C. Al. Stefanescu, Fuzzy objects in topoi, a generalization of fuzzy sets, Bul. Inst, Politehn. Iasi 24 (1978), 25-28.
  15. L. D. Nel, Topological universes and smooth Gelfand-Naimark duality, mathematical applications of category theory, Proc. A.M.S. Spec. Session Denver, 1983, Contemporary Mathematics 30 (1984), 224-276.
  16. A. M. Pittes, Fuzzy sets do not form a topos, Fuzzy Sets and Systems 8 (1982), 235-244. https://doi.org/10.1016/S0165-0114(82)80002-X
  17. D. Ponasse, Fuzzy sets do not form a topos, Fuzzy Sets and Systems 8 (1982), 235-244. https://doi.org/10.1016/S0165-0114(82)80002-X
  18. D. Ponasse, Some remarks on the category Fuz(H) of M. Eytan, Fuzzy Sets and Systems 9 (1983), 199-204. https://doi.org/10.1016/S0165-0114(83)80018-9
  19. L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X