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Interval-Valued H-Fuzzy Sets

  • Lee, Keon-Chang (Department of Computer Science, Dongshin University) ;
  • Lee, Jeong-Gon (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University) ;
  • Hur, Kul (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
  • Received : 2009.10.03
  • Accepted : 2010.05.12
  • Published : 2010.06.25

Abstract

We introduce the category IVSet(H) of interval-valued H-fuzzy sets and show that IVSet(H) satisfies all the conditions of a topological universe except the terminal separator property. And we study some relations among IVSet (H), ISet (H) and Set (H).

Keywords

References

  1. K.T. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems 20, pp. 87-96, 1986. https://doi.org/10.1016/S0165-0114(86)80034-3
  2. G.Birkhoff, Lattice Theory Space(A.M.S.Colloquium Publication Vol XXV, 1967.
  3. J.C.Carrega, "The category Set(H) and Fuz(H)", Fuzzy Sets and Systems 9 , pp. 327-332, 1983. https://doi.org/10.1016/S0165-0114(83)80031-1
  4. E.J.Dubuc, Concrete quasitopoi, Applications of Sheaves. Proc. Dunham 1977, Lect. Notes in Math. 753, pp. 239-254, (1979). https://doi.org/10.1007/BFb0061821
  5. M.Eytan, "Fuzzy sets: a topological point of view", Fuzzy Sets and Systems 5, pp. 47-67, 1981. https://doi.org/10.1016/0165-0114(81)90033-6
  6. J.A.Goguen, "Categories of V-sets", Bull. Amer.Math.Soc. 75, pp. 622-624, 1969. https://doi.org/10.1090/S0002-9904-1969-12267-6
  7. M.B.Gorzalczany, "A method of inference in approximate reasoning based on interval-valued fuzzy sets", Fuzzy Sets and Systems 21 , pp. 1-17, 1987. https://doi.org/10.1016/0165-0114(87)90148-5
  8. H.Herrlich, Cartesian closed topological categories, Math. Coll. Univ. Cape Town 9, pp. 1-16, 1974.
  9. K.Hur, "A note on the category Set(H)", Honam Math.J. 10, pp. 89-94, 1988.
  10. 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) , pp. 33-45, 2005.
  11. P.T.Johnstone, Stone spaces, Cambridge University Press(1982).
  12. 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.
  13. T.K.Mondal and S.K.Samanta, "Topology of interval-valued fuzzy sets", Indian J.Pure Appl. Math. 30, 1, pp. 23-38, 1999.
  14. C.V.Negoita and C.Al. Stefanescu, "Fuzzy objects in topoi, a generalization of fuzzy sets", Bul.Inst. Politehn. Iasi 24, pp. 25-28, 1978.
  15. L.D.Nel, Topological universes and smooth Gelfand-Naimark duality, mathematical applications of category theory, Proc.A.M.S.Spec.Sessopn Denver, 1983, Contemporary Mathematics 30, pp. 224-276, 1984.
  16. J.H.Park, J.S.Park and Y.C.Kwun, "On fuzzy inclusion in the interval-valued sense", FSKG 2005, LANI 3613, Springer-Verlag pp. 1-10, 2005.
  17. A.M. Pittes, "Fuzzy sets do not form a topos", Fuzzy Sets and Systems 8, pp. 338-358, 1982.
  18. D.Ponasse, "Categorical studies of fuzzy sets", Fuzzy Sets and Systems 28, pp. 235-244, 1988. https://doi.org/10.1016/0165-0114(88)90031-0
  19. D.Ponasse, "Some remarks on the category Fuz(H) of M.Eytan", Fuzzy Sets and Systems 9, pp. 199-204, 1983. https://doi.org/10.1016/S0165-0114(83)80018-9
  20. L.A. Zadeh, "Fuzzy sets", Inf. Control. 8, pp. 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X