Picture fuzzy topological spaces and associated continuous functions

Abdul Razaq; Ibtisam Masmali; Harish Garg; Umer Shuaib; Abdul Razaq; Ibtisam Masmali; Harish Garg; Umer Shuaib

doi:10.3934/math.2022814

AIMS Mathematics

2022, Volume 7, Issue 8: 14840-14861. doi: 10.3934/math.2022814

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Research article

Picture fuzzy topological spaces and associated continuous functions

1.
Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
2.
Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia
3.
School of Mathematics Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, Punjab, India
4.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan

Received: 06 February 2022 Revised: 06 May 2022 Accepted: 26 May 2022 Published: 09 June 2022
MSC : 03E72, 08A72, 54A40

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.
- fuzzy sets,
- picture fuzzy sets,
- picture fuzzy topological spaces,
- picture fuzzy topological bases,
- picture fuzzy topological sub-bases,
- continuity
Citation: Abdul Razaq, Ibtisam Masmali, Harish Garg, Umer Shuaib. Picture fuzzy topological spaces and associated continuous functions[J]. AIMS Mathematics, 2022, 7(8): 14840-14861. doi: 10.3934/math.2022814

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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.

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