A study of quadratic Diophantine fuzzy sets with structural properties and their application in face mask detection during COVID-19

Muhammad Danish Zia; Esmail Hassan Abdullatif Al-Sabri; Faisal Yousafzai; Murad-ul-Islam Khan; Rashad Ismail; Mohammed M. Khalaf; Muhammad Danish Zia; Esmail Hassan Abdullatif Al-Sabri; Faisal Yousafzai; Murad-ul-Islam Khan; Rashad Ismail; Mohammed M. Khalaf

doi:10.3934/math.2023738

AIMS Mathematics

2023, Volume 8, Issue 6: 14449-14474. doi: 10.3934/math.2023738

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A study of quadratic Diophantine fuzzy sets with structural properties and their application in face mask detection during COVID-19

1.
Department of Basic Sciences and Humanities, National University of Sciences and Technology, Islamabad, Pakistan
2.
Department of Mathematics, Faculty of Science and Arts, Mahayl Assir, King Khalid University, Abha, Saudi Arabia
3.
Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, Yemen
4.
Department of Mathematics and Statistics, The University of Haripur, Haripur, Pakistan
5.
Department of Mathematics, Higher Institute of Engineering and Technology, King Marriott, Egypt, P.O. Box 3135, Egypt

Received: 25 January 2023 Revised: 11 March 2023 Accepted: 21 March 2023 Published: 19 April 2023
MSC : 03E72, 90B50, 94D05

During the COVID-19 pandemic, identifying face masks with artificial intelligence was a crucial challenge for decision support systems. To address this challenge, we propose a quadratic Diophantine fuzzy decision-making model to rank artificial intelligence techniques for detecting masks, aiming to prevent the global spread of the disease. Our paper introduces the innovative concept of quadratic Diophantine fuzzy sets (QDFSs), which are advanced tools for modeling the uncertainty inherent in a given phenomenon. We investigate the structural properties of QDFSs and demonstrate that they generalize various fuzzy sets. In addition, we introduce essential algebraic operations, set-theoretical operations, and aggregation operators. Finally, we present a numerical case study that applies our proposed algorithms to select a unique face mask detection method and evaluate the effectiveness of our techniques. Our findings demonstrate the viability of our mask identification methodology during the COVID-19 outbreak.
- quadratic Diophantine fuzzy sets,
- COVID-19,
- face mask detection,
- aggregation operators,
- decision-making,
- neural network,
- artificial intelligence
Citation: Muhammad Danish Zia, Esmail Hassan Abdullatif Al-Sabri, Faisal Yousafzai, Murad-ul-Islam Khan, Rashad Ismail, Mohammed M. Khalaf. A study of quadratic Diophantine fuzzy sets with structural properties and their application in face mask detection during COVID-19[J]. AIMS Mathematics, 2023, 8(6): 14449-14474. doi: 10.3934/math.2023738

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Abstract

During the COVID-19 pandemic, identifying face masks with artificial intelligence was a crucial challenge for decision support systems. To address this challenge, we propose a quadratic Diophantine fuzzy decision-making model to rank artificial intelligence techniques for detecting masks, aiming to prevent the global spread of the disease. Our paper introduces the innovative concept of quadratic Diophantine fuzzy sets (QDFSs), which are advanced tools for modeling the uncertainty inherent in a given phenomenon. We investigate the structural properties of QDFSs and demonstrate that they generalize various fuzzy sets. In addition, we introduce essential algebraic operations, set-theoretical operations, and aggregation operators. Finally, we present a numerical case study that applies our proposed algorithms to select a unique face mask detection method and evaluate the effectiveness of our techniques. Our findings demonstrate the viability of our mask identification methodology during the COVID-19 outbreak.

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