Araştırma Makalesi
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N-Fuzzy BI-Topological Space and Separation Axioms

Yıl 2018, Sayı: 25, 8 - 15, 06.10.2018

Faisal Khan Saleem Abdullah Muhammad Rahim Muhammad Shahzad

Öz

In this article, we introduced N-fuzzy bi-topological space by using the concepts
of fuzzy bi-topological space. We further define some basic properties of N-fuzzy bi-topological
spaces, secondly we study the concepts of natural separation axioms of bi-topological in N-fuzzy
bi-topological space which is pair wise separation Axioms mixed topology with the help of two
N-fuzzy topologies of a N-fuzzy bi-topological space. Relation between such pairwise separation
axioms and natural fuzzy separation axioms of the mixed fuzzy topological space are investigated. 

Anahtar Kelimeler

N-fuzzy set N-fuzzy bi-topological space natural separation axioms natural fuzzy separation axioms

Kaynakça

  • [1] L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338-353.
  • [2] N. Palaniappan, Fuzzy topology, Narosa Publications, (2002).
  • [3] C. L. Chang, Fuzzy topological spaces, J Math Anal Appl 24 (1968) 182-192.
  • [4] S. Ganguly and S. Saha, on separation axioms and separation of connected sets in Fuzzy topological space, Bull cal.Math Soc 79 (1987) 215-225.
  • [5] N. R. Das and P. C. Baishya, Fuzzy bi-topological space and separation Axioms, The Jour, Fuzzy Math 2 (1994) 3890-386.
  • [6] R. L. Srivastava and A. K. Srivastava, Fuzzy T1 topological spaces, J Math Anal. Appl 102 (1984) 442-448.
  • [7] A. K. Srivastava, M. Ali, Dewan, A note on K K Azad’s Fuzzy Hausdorffness conceptsn, Fuzzy sets and systems 42 (1991) 363-367.
  • [8] J. C. Kelley, Bi-topological Spaces, Inoc London Math. Soc 3 ( 1963) 781-89.
  • [9] J. Mahanta and P. K. Das, Results on Fuzzy soft topological space, Math. G.M March -3 (2012) PP1-11.
  • [10] T. J. Neog, D. K. Sut and G. C. Hazarika, Fuzzy soft topological Space, Int. J. Latest Trend Math Vol.2 No.1 March (2012).
  • [11] R. Srivastava, On separation axioms in a newly defined fuzzy topology, Fuzzy Sets and Systems, 62 (1994) 341-346.
  • [12] R. Srivastava, M. Srivastava, On pairwise Hausdorff fuzzy bitopological spaces5, J. of Fuzzy Math, 5 (1997) 553-564.
  • [13] R. Srivastava, M. Srivastava, On certain separation axioms in fuzzy bitopological spaces, Far East Journal of Math. Sciences, 27 (2007) 579-587.
  • [14] A. K. Srivastava, R. Srivastava, Sierpinski object in fuzzy topology, in: Proc. Int. Symp. on Modern Anal. and Appls. (Conf. Proc.), Prentice-Hall of India, (1985) 17- 25.
  • [15] R. Srivastava, S. N. Lal and A. K. Srivastava, On fuzzy T0 and R0 topological spaces, Journal of Mathematical Analysis and Applications, 136 (1988) 6673.
  • [16] R. Srivastava, S. N. Lal and A. K. Srivastava, Fuzzy Hausdorff topological spaces, Journal of Mathematical Analysis and Applications, 81 (1981) 497506.
  • [17] R. Lowen, Fuzzy topological spaces and fuzzy compactness, Journal of Mathematical Analysis and Applications, 56 (1976) 621633.
  • [18] S. Carlson, Fuzzy topological spaces, Part 1: Fuzzy sets and fuzzy topologies, Early ideas and obstacles, Rose-Hulman Institute of Technology.
  • [19] S. Willard, General Topology, Dover Publications, New York, 2004.
  • [20] B. C. Tripathy and A. Baruah, Lacunary statically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers. Kyungpook Mathematical Journal, 50(4),(2010) 565-574.
  • [21] B. C. Tripathy, A. Baruah, M. Et and M. Gungor, On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers. Iranian Journal of Science and Technology (Sciences), 36(2), (2012) 147-155.
  • [22] B. C. Tripathy and A. J. Dutta, Lacunary bounded variation sequence of fuzzy real numbers. Journal of Intelligent and Fuzzy Systems, 24(1), (2013) 185-189.
  • [23] B. C. Tripathy, J. D. Sarma, On weakly b-continuous functions in bitopological spaces. Acta Scientiarum. Technology, 35(3), (2013).
  • [24] B. C. Tripathy ans S. Acharjee, On (Y, d)-Bitopological semi-closed set via topological ideal. Proyecciones. Journal of Mathematics, 33(3), (2014) 245-257.
  • [25] B. C. Tripathy and S. Debnath, Y-open sets and Y-continuous mappings in fuzzy bitopological spaces. Journal of Intelligent and Fuzzy Systems, 24(3), (2013) 631-635.

Yıl 2018, Sayı: 25, 8 - 15, 06.10.2018

Faisal Khan Saleem Abdullah Muhammad Rahim Muhammad Shahzad

Öz

Kaynakça

  • [1] L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338-353.
  • [2] N. Palaniappan, Fuzzy topology, Narosa Publications, (2002).
  • [3] C. L. Chang, Fuzzy topological spaces, J Math Anal Appl 24 (1968) 182-192.
  • [4] S. Ganguly and S. Saha, on separation axioms and separation of connected sets in Fuzzy topological space, Bull cal.Math Soc 79 (1987) 215-225.
  • [5] N. R. Das and P. C. Baishya, Fuzzy bi-topological space and separation Axioms, The Jour, Fuzzy Math 2 (1994) 3890-386.
  • [6] R. L. Srivastava and A. K. Srivastava, Fuzzy T1 topological spaces, J Math Anal. Appl 102 (1984) 442-448.
  • [7] A. K. Srivastava, M. Ali, Dewan, A note on K K Azad’s Fuzzy Hausdorffness conceptsn, Fuzzy sets and systems 42 (1991) 363-367.
  • [8] J. C. Kelley, Bi-topological Spaces, Inoc London Math. Soc 3 ( 1963) 781-89.
  • [9] J. Mahanta and P. K. Das, Results on Fuzzy soft topological space, Math. G.M March -3 (2012) PP1-11.
  • [10] T. J. Neog, D. K. Sut and G. C. Hazarika, Fuzzy soft topological Space, Int. J. Latest Trend Math Vol.2 No.1 March (2012).
  • [11] R. Srivastava, On separation axioms in a newly defined fuzzy topology, Fuzzy Sets and Systems, 62 (1994) 341-346.
  • [12] R. Srivastava, M. Srivastava, On pairwise Hausdorff fuzzy bitopological spaces5, J. of Fuzzy Math, 5 (1997) 553-564.
  • [13] R. Srivastava, M. Srivastava, On certain separation axioms in fuzzy bitopological spaces, Far East Journal of Math. Sciences, 27 (2007) 579-587.
  • [14] A. K. Srivastava, R. Srivastava, Sierpinski object in fuzzy topology, in: Proc. Int. Symp. on Modern Anal. and Appls. (Conf. Proc.), Prentice-Hall of India, (1985) 17- 25.
  • [15] R. Srivastava, S. N. Lal and A. K. Srivastava, On fuzzy T0 and R0 topological spaces, Journal of Mathematical Analysis and Applications, 136 (1988) 6673.
  • [16] R. Srivastava, S. N. Lal and A. K. Srivastava, Fuzzy Hausdorff topological spaces, Journal of Mathematical Analysis and Applications, 81 (1981) 497506.
  • [17] R. Lowen, Fuzzy topological spaces and fuzzy compactness, Journal of Mathematical Analysis and Applications, 56 (1976) 621633.
  • [18] S. Carlson, Fuzzy topological spaces, Part 1: Fuzzy sets and fuzzy topologies, Early ideas and obstacles, Rose-Hulman Institute of Technology.
  • [19] S. Willard, General Topology, Dover Publications, New York, 2004.
  • [20] B. C. Tripathy and A. Baruah, Lacunary statically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers. Kyungpook Mathematical Journal, 50(4),(2010) 565-574.
  • [21] B. C. Tripathy, A. Baruah, M. Et and M. Gungor, On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers. Iranian Journal of Science and Technology (Sciences), 36(2), (2012) 147-155.
  • [22] B. C. Tripathy and A. J. Dutta, Lacunary bounded variation sequence of fuzzy real numbers. Journal of Intelligent and Fuzzy Systems, 24(1), (2013) 185-189.
  • [23] B. C. Tripathy, J. D. Sarma, On weakly b-continuous functions in bitopological spaces. Acta Scientiarum. Technology, 35(3), (2013).
  • [24] B. C. Tripathy ans S. Acharjee, On (Y, d)-Bitopological semi-closed set via topological ideal. Proyecciones. Journal of Mathematics, 33(3), (2014) 245-257.
  • [25] B. C. Tripathy and S. Debnath, Y-open sets and Y-continuous mappings in fuzzy bitopological spaces. Journal of Intelligent and Fuzzy Systems, 24(3), (2013) 631-635.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Faisal Khan

Saleem Abdullah

Muhammad Rahim

Muhammad Shahzad

Yayımlanma Tarihi 6 Ekim 2018
Gönderilme Tarihi 31 Mart 2018
Yayımlandığı Sayı Yıl 2018 Sayı: 25

Kaynak Göster

APA Khan, F., Abdullah, S., Rahim, M., Shahzad, M. (2018). N-Fuzzy BI-Topological Space and Separation Axioms. Journal of New Theory(25), 8-15.
AMA Khan F, Abdullah S, Rahim M, Shahzad M. N-Fuzzy BI-Topological Space and Separation Axioms. JNT. Ekim 2018;(25):8-15.
Chicago Khan, Faisal, Saleem Abdullah, Muhammad Rahim, ve Muhammad Shahzad. “N-Fuzzy BI-Topological Space and Separation Axioms”. Journal of New Theory, sy. 25 (Ekim 2018): 8-15.
EndNote Khan F, Abdullah S, Rahim M, Shahzad M (01 Ekim 2018) N-Fuzzy BI-Topological Space and Separation Axioms. Journal of New Theory 25 8–15.
IEEE F. Khan, S. Abdullah, M. Rahim, ve M. Shahzad, “N-Fuzzy BI-Topological Space and Separation Axioms”, JNT, sy. 25, ss. 8–15, Ekim 2018.
ISNAD Khan, Faisal vd. “N-Fuzzy BI-Topological Space and Separation Axioms”. Journal of New Theory 25 (Ekim 2018), 8-15.
JAMA Khan F, Abdullah S, Rahim M, Shahzad M. N-Fuzzy BI-Topological Space and Separation Axioms. JNT. 2018;:8–15.
MLA Khan, Faisal vd. “N-Fuzzy BI-Topological Space and Separation Axioms”. Journal of New Theory, sy. 25, 2018, ss. 8-15.
Vancouver Khan F, Abdullah S, Rahim M, Shahzad M. N-Fuzzy BI-Topological Space and Separation Axioms. JNT. 2018(25):8-15.
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