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On Intuitionistic Zero Gradations

Year 2015, Volume: 36 Issue: 3, 1752 - 1760, 13.05.2015

Mohammad Abry , Jafar Zanjanı

Abstract

Abstract. In this paper, we introduce the concept of an intuitionistic zero gradation in Lowen fuzzy topological spaces. We study some relations between the notion of zero-dimensionality of fuzzy bitopological spaces and intuition- istic zero gradations and then prove that the property of being intuitionistic zero gradation is invariant under a strongly gradation preserving map.

Keywords

Fuzzy topology Gradation of openness Intuitionistic gradation of openness Intuitionistic zero gradation Zero-dimension

References

  • A.S. Abu Sa.ya, A.A. Fora and M.W. Warner, Higher separation axioms in bifuzzy topological spaces, Fuzzy sets and systems 79 (1996) 367–372.
  • D. Adnadjevic, Dimension of fuzzy spaces, Fuzzy sets and systems. 26 (1988) 85– 92.
  • K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and systems. 20 (1986), no. 1, 87–96.
  • C.L. Chang, Fuzzy topological spaces, J.Math.Anal.Appl. 24(1968) 182–190.
  • K.C. Chattopadhyay, R.N. Hazra and S.K. Samanta, Gradation of openness; Fuzzy topology, Fuzzy sets and systems. 49(1992) 237–242
  • D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy sets and systems. 88 (1997) 81–89.
  • E. Cuchillo-Ibanez, J. Tarres, On the boundary of fuzzy sets, Fuzzy sets and systems. 89 (1997) 113–119.
  • S. K. De, R. Biswas, and A. R. Roy, An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems, 117 (2001), no. 2, 209–213.
  • R. Engelking, Dimension Theory, North-Holland, Amsterdam, (1978).
  • B. Hutton, Products of fuzzy topological spaces, Top. Appl. 11 (1980) 59–67.
  • Kandil, A.A. Nouh and S.A. El-Sheikh, On fuzzy bitopological spaces, Fuzzy sets and systems. 74 (1995) 353–363.
  • R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math.Anal.Appl. 56 (1976) 621–633.
  • T. K. Mondal and S. K. Samanta, On intuitionistic gradation of openness, Fuzzy sets and systems. 131 (2002) 323–336.
  • L. G. Oversteegen and E. D. Tymchatyn, On the dimension of certain totally disconnected spaces, Proc. Amer. Math. Soc. 122 (1994) 885–891.
  • R. Srivastava, S. N. Lal, and A. K. Srivastava, Fuzzy Hausdorff topological spaces, J.Math.Anal.Appl. 81 (1981) 497–506.
  • L.A. Zadeh, Fuzzy sets, Information and control. 8 (1965) 338–353.

Year 2015, Volume: 36 Issue: 3, 1752 - 1760, 13.05.2015

Mohammad Abry , Jafar Zanjanı

Abstract

References

  • A.S. Abu Sa.ya, A.A. Fora and M.W. Warner, Higher separation axioms in bifuzzy topological spaces, Fuzzy sets and systems 79 (1996) 367–372.
  • D. Adnadjevic, Dimension of fuzzy spaces, Fuzzy sets and systems. 26 (1988) 85– 92.
  • K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and systems. 20 (1986), no. 1, 87–96.
  • C.L. Chang, Fuzzy topological spaces, J.Math.Anal.Appl. 24(1968) 182–190.
  • K.C. Chattopadhyay, R.N. Hazra and S.K. Samanta, Gradation of openness; Fuzzy topology, Fuzzy sets and systems. 49(1992) 237–242
  • D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy sets and systems. 88 (1997) 81–89.
  • E. Cuchillo-Ibanez, J. Tarres, On the boundary of fuzzy sets, Fuzzy sets and systems. 89 (1997) 113–119.
  • S. K. De, R. Biswas, and A. R. Roy, An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems, 117 (2001), no. 2, 209–213.
  • R. Engelking, Dimension Theory, North-Holland, Amsterdam, (1978).
  • B. Hutton, Products of fuzzy topological spaces, Top. Appl. 11 (1980) 59–67.
  • Kandil, A.A. Nouh and S.A. El-Sheikh, On fuzzy bitopological spaces, Fuzzy sets and systems. 74 (1995) 353–363.
  • R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math.Anal.Appl. 56 (1976) 621–633.
  • T. K. Mondal and S. K. Samanta, On intuitionistic gradation of openness, Fuzzy sets and systems. 131 (2002) 323–336.
  • L. G. Oversteegen and E. D. Tymchatyn, On the dimension of certain totally disconnected spaces, Proc. Amer. Math. Soc. 122 (1994) 885–891.
  • R. Srivastava, S. N. Lal, and A. K. Srivastava, Fuzzy Hausdorff topological spaces, J.Math.Anal.Appl. 81 (1981) 497–506.
  • L.A. Zadeh, Fuzzy sets, Information and control. 8 (1965) 338–353.
There are 16 citations in total.

Details

Journal Section Special
Authors

Mohammad Abry

Jafar Zanjanı This is me

Publication Date May 13, 2015
Published in Issue Year 2015 Volume: 36 Issue: 3

Cite

APA Abry, M., & Zanjanı, J. (2015). On Intuitionistic Zero Gradations. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, 36(3), 1752-1760.
AMA Abry M, Zanjanı J. On Intuitionistic Zero Gradations. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. May 2015;36(3):1752-1760.
Chicago Abry, Mohammad, and Jafar Zanjanı. “On Intuitionistic Zero Gradations”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36, no. 3 (May 2015): 1752-60.
EndNote Abry M, Zanjanı J (May 1, 2015) On Intuitionistic Zero Gradations. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36 3 1752–1760.
IEEE M. Abry and J. Zanjanı, “On Intuitionistic Zero Gradations”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 3, pp. 1752–1760, 2015.
ISNAD Abry, Mohammad - Zanjanı, Jafar. “On Intuitionistic Zero Gradations”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36/3 (May2015), 1752-1760.
JAMA Abry M, Zanjanı J. On Intuitionistic Zero Gradations. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36:1752–1760.
MLA Abry, Mohammad and Jafar Zanjanı. “On Intuitionistic Zero Gradations”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 3, 2015, pp. 1752-60.
Vancouver Abry M, Zanjanı J. On Intuitionistic Zero Gradations. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36(3):1752-60.