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International Journal of Fuzzy Logic and Intelligent Systems 2020; 20(1): 77-86

Published online March 25, 2020

https://doi.org/10.5391/IJFIS.2020.20.1.77

© The Korean Institute of Intelligent Systems

On Separation Axioms in Fuzzifying Bitopological Spaces

Ahmed Abd El-Monsef Allam1, Ahmed Mohammed Zahran2, Ahmed Khalf Mousa2;3, and Hana Mohsen Binshahnah4

1Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
2Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt
3Department of Mathematics, University of Tabuk at Al-Wajh, Saudi Arabia
4Department of Mathematics, Faculty of Science, Hadhramout University, Republic of Yemen

Correspondence to :
Ahmed Khalf Mousa (akmousa@azhar.edu.eg)

Received: September 18, 2019; Revised: December 18, 2019; Accepted: March 11, 2020

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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In present paper, we introduce and study the concepts of T0(i,j)-,T1(i,j)-,T2(i,j) (pairwise Hausdorff)-,TR(i,j) (pairwise regularity)-,TN(i,j) (pairwise normality)-,R0(i,j)-,R1(i,j)-,T3(i,j)- and T4(i,j)- separation axioms in fuzzifying bitopological spaces and study some relations between them. Also we investigate the image of these kinds of fuzzifying bitopological spaces under some types of fuzzy mappings.

Keywords: Fuzzifying topology, Fuzzifying bitopological space, Separation axioms

Biographies

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Ahmed Abd El-Monsef Allam s a professor of Department of Mathematics, Assiut University, Egypt. His research areas are fuzzy topology and general topology.

E-mail: allam51ahmed@yahoo.com


Ahmed Mohammed Zahran is a professor of Department of Mathematics, Al-Azhar University, Egypt. His research areas are fuzzy topology and general topology.

E-mail: amzahran@azhar.edu.eg


Ahmed Khalf Mousa is a associate professor of Department of Mathematics, Al-Azhar University, Egypt. His research areas are fuzzy topology, general topology, and GIS.

E-mail: akmousa@azhar.edu.eg


Hana Mohsen Binshahnah is a assistant professor of Department of Mathematics, Hadhramout University, Yemen. His research areas are fuzzy topology and general topology.

E-mail: hmbsh2006@yahoo.com


Article

Original Article

International Journal of Fuzzy Logic and Intelligent Systems 2020; 20(1): 77-86

Published online March 25, 2020 https://doi.org/10.5391/IJFIS.2020.20.1.77

Copyright © The Korean Institute of Intelligent Systems.

On Separation Axioms in Fuzzifying Bitopological Spaces

Ahmed Abd El-Monsef Allam1, Ahmed Mohammed Zahran2, Ahmed Khalf Mousa2;3, and Hana Mohsen Binshahnah4

1Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
2Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt
3Department of Mathematics, University of Tabuk at Al-Wajh, Saudi Arabia
4Department of Mathematics, Faculty of Science, Hadhramout University, Republic of Yemen

Correspondence to:Ahmed Khalf Mousa (akmousa@azhar.edu.eg)

Received: September 18, 2019; Revised: December 18, 2019; Accepted: March 11, 2020

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In present paper, we introduce and study the concepts of T0(i,j)-,T1(i,j)-,T2(i,j) (pairwise Hausdorff)-,TR(i,j) (pairwise regularity)-,TN(i,j) (pairwise normality)-,R0(i,j)-,R1(i,j)-,T3(i,j)- and T4(i,j)- separation axioms in fuzzifying bitopological spaces and study some relations between them. Also we investigate the image of these kinds of fuzzifying bitopological spaces under some types of fuzzy mappings.

Keywords: Fuzzifying topology, Fuzzifying bitopological space, Separation axioms

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