A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces

S. Jothimani; T. Jenitha Premalatha

doi:doi:10.11648/j.mcs.20170202.11

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A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces

S. Jothimani, T. Jenitha Premalatha

Published in Mathematics and Computer Science (Volume 2, Issue 2)

Received: 22 April 2017 Accepted: 4 May 2017 Published: 27 June 2017

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Abstract

In this paper we introduce the concept of (i,j)–πgβ-closed set in intuitionistic fuzzy bitopological spaces as a generalization of πgβ-closed set in fuzzy bitopological space and study their related notions in bitopological spaces. Next, we introduce (i,j)–πgβ- open sets in intuitionistic fuzzy bitopological spaces, and investigate some of their basic properties. Using these concepts, the characterizations for the intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are obtained. The relationships between intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are discussed. Finally, we prove the irresoluteness in (i,j)–πgβ intuitionistic fuzzy bitopological spaces.

Published in	Mathematics and Computer Science (Volume 2, Issue 2)
DOI	10.11648/j.mcs.20170202.11
Page(s)	14-19
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

IF Bitopological Spaces, IF (i, j)β-Open Sets, IF(i, j)β-Closed Sets, IF (I,j) πgβ-Open Sets, IF (i,j) πgβ-Closed Sets, IF (i,j) πgβ-Pairwise Continuous Function and IF (i,j) πgβ-Irresolute Function

References

[1]	Abd. El-Monsef. M. E, El Deeb. S. N. and Mahmoud. R. A, “-open sets and-continuous mappings”, Bull. Fac. Sci. Assiut Univ., 12 (1983), 77-90.
[2]	Andrijevic. D, “Semi-preopen sets” Mat. Vesnik, 38 (1986), no. 1, 24-32.
[3]	K. Atanassova, S. Stoeva, Intuitionistic Fuzzy Sets, In Polish Symposium on Interval and Fuzzy MathematicsPoznan (1983) 23-26.
[4]	M. Caldas and S. Jafari - Weak and strong forms of  Irresoluteness - The Arabian Journal for Science and Engineering, Volume 31, Number 1A-31-39.
[5]	D. Coker, An Introduction to Intuitionistic Fuzzy Topological Spaces, Fuzzy Sets and Systems 88(1997) 81-89.
[6]	Jin Tae Kim, Seok Jong Lee- Some Properties of Intuitionistic Fuzzy Bitopological Spaces- SCIS-ISIS 2012, Kobe, Japan, November 20-24, 2012.
[7]	A. Kandil, “Biproximities and fuzzy bitopological spaces,” Simon Stevin, vol. 63, pp. 45–66, 1989.
[8]	J. C. Kelly, Bitopological spaces, Proc. London Math. Soc., 13, 71-89 (1963).
[9]	Raja Rajeswari. R and Lellis Thivagar. M, “On Extension of Semi-pre open sets in Bitopological Spaces”, Proc. of the National Conference in Pure and Applied Mathematics, (2005), 28-32.

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APA Style

S. Jothimani, T. Jenitha Premalatha. (2017). A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces. Mathematics and Computer Science, 2(2), 14-19. https://doi.org/10.11648/j.mcs.20170202.11

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ACS Style

S. Jothimani; T. Jenitha Premalatha. A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces. Math. Comput. Sci. 2017, 2(2), 14-19. doi: 10.11648/j.mcs.20170202.11

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AMA Style

S. Jothimani, T. Jenitha Premalatha. A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces. Math Comput Sci. 2017;2(2):14-19. doi: 10.11648/j.mcs.20170202.11

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@article{10.11648/j.mcs.20170202.11,
  author = {S. Jothimani and T. Jenitha Premalatha},
  title = {A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces},
  journal = {Mathematics and Computer Science},
  volume = {2},
  number = {2},
  pages = {14-19},
  doi = {10.11648/j.mcs.20170202.11},
  url = {https://doi.org/10.11648/j.mcs.20170202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20170202.11},
  abstract = {In this paper we introduce the concept of (i,j)–πgβ-closed set in intuitionistic fuzzy bitopological spaces as a generalization of πgβ-closed set in fuzzy bitopological space and study their related notions in bitopological spaces. Next, we introduce (i,j)–πgβ- open sets in intuitionistic fuzzy bitopological spaces, and investigate some of their basic properties. Using these concepts, the characterizations for the intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are obtained. The relationships between intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are discussed. Finally, we prove the irresoluteness in (i,j)–πgβ intuitionistic fuzzy bitopological spaces.},
 year = {2017}
}

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TY  - JOUR
T1  - A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces
AU  - S. Jothimani
AU  - T. Jenitha Premalatha
Y1  - 2017/06/27
PY  - 2017
N1  - https://doi.org/10.11648/j.mcs.20170202.11
DO  - 10.11648/j.mcs.20170202.11
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
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PB  - Science Publishing Group
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AB  - In this paper we introduce the concept of (i,j)–πgβ-closed set in intuitionistic fuzzy bitopological spaces as a generalization of πgβ-closed set in fuzzy bitopological space and study their related notions in bitopological spaces. Next, we introduce (i,j)–πgβ- open sets in intuitionistic fuzzy bitopological spaces, and investigate some of their basic properties. Using these concepts, the characterizations for the intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are obtained. The relationships between intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are discussed. Finally, we prove the irresoluteness in (i,j)–πgβ intuitionistic fuzzy bitopological spaces.
VL  - 2
IS  - 2
ER  -

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Author Information

S. Jothimani

Department of Mathematics, Government Arts and Science College, Coimbatore, India
T. Jenitha Premalatha

KPR Institute of Engineering and Technology, Coimbatore, India

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APA Style

S. Jothimani, T. Jenitha Premalatha. (2017). A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces. Mathematics and Computer Science, 2(2), 14-19. https://doi.org/10.11648/j.mcs.20170202.11

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ACS Style

S. Jothimani; T. Jenitha Premalatha. A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces. Math. Comput. Sci. 2017, 2(2), 14-19. doi: 10.11648/j.mcs.20170202.11

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AMA Style

S. Jothimani, T. Jenitha Premalatha. A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces. Math Comput Sci. 2017;2(2):14-19. doi: 10.11648/j.mcs.20170202.11

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@article{10.11648/j.mcs.20170202.11,
  author = {S. Jothimani and T. Jenitha Premalatha},
  title = {A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces},
  journal = {Mathematics and Computer Science},
  volume = {2},
  number = {2},
  pages = {14-19},
  doi = {10.11648/j.mcs.20170202.11},
  url = {https://doi.org/10.11648/j.mcs.20170202.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20170202.11},
  abstract = {In this paper we introduce the concept of (i,j)–πgβ-closed set in intuitionistic fuzzy bitopological spaces as a generalization of πgβ-closed set in fuzzy bitopological space and study their related notions in bitopological spaces. Next, we introduce (i,j)–πgβ- open sets in intuitionistic fuzzy bitopological spaces, and investigate some of their basic properties. Using these concepts, the characterizations for the intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are obtained. The relationships between intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are discussed. Finally, we prove the irresoluteness in (i,j)–πgβ intuitionistic fuzzy bitopological spaces.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - A Note on (i,j)-πgβ Closed Sets in Intuitionistic Fuzzy Bitopological Spaces
AU  - S. Jothimani
AU  - T. Jenitha Premalatha
Y1  - 2017/06/27
PY  - 2017
N1  - https://doi.org/10.11648/j.mcs.20170202.11
DO  - 10.11648/j.mcs.20170202.11
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 14
EP  - 19
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20170202.11
AB  - In this paper we introduce the concept of (i,j)–πgβ-closed set in intuitionistic fuzzy bitopological spaces as a generalization of πgβ-closed set in fuzzy bitopological space and study their related notions in bitopological spaces. Next, we introduce (i,j)–πgβ- open sets in intuitionistic fuzzy bitopological spaces, and investigate some of their basic properties. Using these concepts, the characterizations for the intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are obtained. The relationships between intuitionistic fuzzy pairwise (i,j)–πgβ continuous mappings are discussed. Finally, we prove the irresoluteness in (i,j)–πgβ intuitionistic fuzzy bitopological spaces.
VL  - 2
IS  - 2
ER  -

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