N-Fuzzy BI-Topological Space and Separation Axioms

Faisal Khan; Saleem Abdullah; Muhammad Rahim; Muhammad Shahzad

EN

N-Fuzzy BI-Topological Space and Separation Axioms

Abstract

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.

Keywords

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

References

[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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Faisal Khan This is me

Saleem Abdullah This is me

Muhammad Rahim This is me

Muhammad Shahzad This is me

Publication Date

October 6, 2018

Submission Date

March 31, 2018

Acceptance Date

-

Published in Issue

Year 2018 Number: 25

IZ

https://izlik.org/JA44ZG32SN

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. https://izlik.org/JA44ZG32SN

AMA

1.Khan F, Abdullah S, Rahim M, Shahzad M. N-Fuzzy BI-Topological Space and Separation Axioms. JNT. 2018;(25):8-15. https://izlik.org/JA44ZG32SN

Chicago

Khan, Faisal, Saleem Abdullah, Muhammad Rahim, and Muhammad Shahzad. 2018. “N-Fuzzy BI-Topological Space and Separation Axioms”. Journal of New Theory, nos. 25: 8-15. https://izlik.org/JA44ZG32SN.

EndNote

Khan F, Abdullah S, Rahim M, Shahzad M (October 1, 2018) N-Fuzzy BI-Topological Space and Separation Axioms. Journal of New Theory 25 8–15.

IEEE

[1]F. Khan, S. Abdullah, M. Rahim, and M. Shahzad, “N-Fuzzy BI-Topological Space and Separation Axioms”, JNT, no. 25, pp. 8–15, Oct. 2018, [Online]. Available: https://izlik.org/JA44ZG32SN

ISNAD

Khan, Faisal - Abdullah, Saleem - Rahim, Muhammad - Shahzad, Muhammad. “N-Fuzzy BI-Topological Space and Separation Axioms”. Journal of New Theory. 25 (October 1, 2018): 8-15. https://izlik.org/JA44ZG32SN.

JAMA

1.Khan F, Abdullah S, Rahim M, Shahzad M. N-Fuzzy BI-Topological Space and Separation Axioms. JNT. 2018;:8–15.

MLA

Khan, Faisal, et al. “N-Fuzzy BI-Topological Space and Separation Axioms”. Journal of New Theory, no. 25, Oct. 2018, pp. 8-15, https://izlik.org/JA44ZG32SN.

Vancouver

1.Faisal Khan, Saleem Abdullah, Muhammad Rahim, Muhammad Shahzad. N-Fuzzy BI-Topological Space and Separation Axioms. JNT [Internet]. 2018 Oct. 1;(25):8-15. Available from: https://izlik.org/JA44ZG32SN