Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Intuitionistic Smooth Topological Spaces

  • Lim, Pyung-Ki (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University) ;
  • Kim, So-Ra (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)
  • 임평기 (원광대학교 수학정보 통계학부) ;
  • 김소라 (원광대학교 대학원 수학과) ;
  • 허걸 (원광대학교 수학정보 통계학부)
  • Received : 2010.10.21
  • Accepted : 2010.11.29
  • Published : 2010.12.25
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Abstract

We introduce the concept of intuitionistic smooth topology in Lowen's sense and we prove that the family IST(X) of all intuitionistic smooth topologies on a set is a meet complete lattice with least element and the greatest element [Proposition 3.6]. Also we introduce the notion of level fuzzy topology on a set X with respect to an intuitionistic smooth topology and we obtain the relation between the intuitionistic smooth topology $\tau$ and the intuitionistic smooth topology $\eta$ generated by level fuzzy topologies with respect to $\tau$ [Theorem 3.10].

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References

  1. S.E.Abbas, "On intuitionistic fuzzy compactness",Inform. Sci. vol. 173, pp. 75-91, 2005. https://doi.org/10.1016/j.ins.2004.07.004
  2. K.T.Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, vol. 20, pp. 87-96, 1986. https://doi.org/10.1016/S0165-0114(86)80034-3
  3. C.L.Chang, "Fuzzy topological spaces", J. Math.Anal.Appl. vol. 24 , pp. 182-190, 1968. https://doi.org/10.1016/0022-247X(68)90057-7
  4. K.C.Chattopadhyay, R.N.Hazra and S.K. Samanta, "Gradation of openness : fuzzy topology", Fuzzy Sets and System, vol. 49, pp. 237-242,1992. https://doi.org/10.1016/0165-0114(92)90329-3
  5. K.C.Chattopadhyay and S.K.Samanta, "Fuzzy topology: fuzzy closure, operator, fuzzy compactness and fuzzy connecteness", Fuzzy Sets and System, vol.54, pp. 207-212, 1992.
  6. T.Kubiak, On fuzzy topologies, Ph.D.Thesis,A.Mickiewicz,Poznan, 1985.
  7. M.Cheong and K.Hur, "Intuitionistic intervalvalued fuzzy sets", To appears in I.Korean Institute of Intelligent Systems, vol.20, no. 6, 2010.
  8. RLowen, "Fuzzy topological spaces and fuzzy compactness", J. Math. Anal. Appl. vol. 56, pp. 621-633, 1976. https://doi.org/10.1016/0022-247X(76)90029-9
  9. T.K.Mondal and S.K.Samanta, "On intuitionistic gradation of openness", Fuzzy Sets and Systems, vol. 131 , pp. 323-336, 2002. https://doi.org/10.1016/S0165-0114(01)00235-4
  10. W.Peeters, "The complete lattice (S(X),${\leq}$) of smooth fuzzy topologies", Fuzzy Sets and System,vol. 125, pp. 145-152, 2002. https://doi.org/10.1016/S0165-0114(01)00030-6
  11. W.Peeters, "Subspaces of smooth fuzzy topologies and initial smooth fuzzy structures", Fuzzy Sets and Systems, vol. 104 , pp. 423-433, 1999. https://doi.org/10.1016/S0165-0114(98)00318-2
  12. P.M.Pu and Y.M.Liu, "Fuzzy topology I." Neighborhood structure of a fuzzy point, J.Math.Anal.Appl. vol. 76 , pp. 571-599, 1982.
  13. P.M.Pu and Y.M.Liu, "Fuzzy topology II. Products and quotient spaces", J.Math.Anal.Appl. vol.77 , pp. 20-37, 1980. https://doi.org/10.1016/0022-247X(80)90258-9
  14. A.A.Ramaden, "Smooth topological spaces", Fuzzy Sets and Systems, vol. 48, pp. 371-375, 1992.
  15. A.P.Sostak, "On a fuzzy topological structure", Suppl.Rend. Circ. Math. Palerms Ser.II, vol. 11 ,pp. 89-103, 1985.
  16. A.P.Sostak, "Two decades of fuzzy topology :basic ideas", notion and results. Russ. Math. Surv. vol. 44, no. 6, pp. 125-186, 1989. https://doi.org/10.1070/RM1989v044n06ABEH002295
  17. A.P.Sostak, "On some modifications of fuzzy topologies", Mathematicki Vesnik, vol. 41, pp. 20-37, 1989.
  18. A.P.Sostak, "On the neighborhood structure of fuzzy topologies", Zb.Radova Univ. Nisu, vol. 4, pp. 7-14, 1990.
  19. T.H.Yalvac, "Fuzzy sets and functions on fuzzy spaces", J. Math. Anal. vo1.126, pp. 409-423, 1987. https://doi.org/10.1016/0022-247X(87)90050-3
  20. L.A.Zadeh, "Fuzzy Sets", Inform. and Control,vol. 8, pp. 338-353,1965. https://doi.org/10.1016/S0019-9958(65)90241-X

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