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Research Article | Open Access

Picture fuzzy topological spaces and associated continuous functions

Abdul Razaq1, Ibtisam Masmali2, Harish Garg3( ), Umer Shuaib4
Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
School of Mathematics Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, Punjab, India
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
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Abstract

This paper describes a study of picture fuzzy topological spaces. We prove some basic results related to picture fuzzy sets together with the introduction of new notions such as the rank, picture fuzzy base and picture fuzzy sub-base of picture fuzzy topological spaces. With the help of these notions, we present a method to design picture fuzzy topological spaces. Furthermore, we introduce the concept of continuity to picture fuzzy topological spaces and find a necessary and sufficient condition for a picture fuzzy continuous function between two picture fuzzy topological spaces.

Keywords

fuzzy setspicture fuzzy setspicture fuzzy topological spacespicture fuzzy topological basespicture fuzzy topological sub-basescontinuity
CLC number: 03E72, 08A72, 54A40

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AIMS Mathematics
Volume 7 Issue 8,
August 2022
Pages 14840-14861
DOI: 10.3934/math.2022814

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Cite this article:
Razaq A, Masmali I, Garg H, et al. Picture fuzzy topological spaces and associated continuous functions. AIMS Mathematics, 2022, 7(8): 14840-14861. https://doi.org/10.3934/math.2022814

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Received: 06 February 2022
Revised: 06 May 2022
Accepted: 26 May 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)