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AIMS Mathematics

2024, Volume 9, Issue 5: 11180-11193. doi: 10.3934/math.2024548
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Soft rough fuzzy sets based on covering

  • 1.
    Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt; Email: roshdeymareay@sci.kfs.edu.eg
  • 2.
    Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13132, Jordan; Email: rgdairi@zu.edu.jo
  • 3.
    Department of Mathematics, Faculty of Science, New Valley University, Egypt; Email: m.shaban@sci.nvu.edu.eg
  • Received: 30 December 2023 Revised: 08 March 2024 Accepted: 15 March 2024 Published: 21 March 2024

  • MSC : 54A40, 03E72, 54C08

  • Soft rough fuzzy sets ($ \mathcal SRFSs $) represent a powerful paradigm that integrates soft computing, rough set theory, and fuzzy logic. This research aimed to comprehensively investigate the various dimensions of $ \mathcal SRFSs $ within the domain of approximation structures. The study encompassed a wide spectrum of concepts, ranging from covering approximation structures and soft rough coverings to soft neighborhoods, fuzzy covering approximation operators, and soft fuzzy covering approximation operators. We introduced three models of $ \mathcal SRFSs $ based on covering via the core of soft neighborhood. We discussed and analyzed our models' characteristics and properties. The relations between our models for soft fuzzy covering sets and Zhan's model for soft rough fuzzy covering were presented.

    Citation: R. Mareay, Radwan Abu-Gdairi, M. Badr. Soft rough fuzzy sets based on covering[J]. AIMS Mathematics, 2024, 9(5): 11180-11193. doi: 10.3934/math.2024548

    Related Papers:

  • Soft rough fuzzy sets ($ \mathcal SRFSs $) represent a powerful paradigm that integrates soft computing, rough set theory, and fuzzy logic. This research aimed to comprehensively investigate the various dimensions of $ \mathcal SRFSs $ within the domain of approximation structures. The study encompassed a wide spectrum of concepts, ranging from covering approximation structures and soft rough coverings to soft neighborhoods, fuzzy covering approximation operators, and soft fuzzy covering approximation operators. We introduced three models of $ \mathcal SRFSs $ based on covering via the core of soft neighborhood. We discussed and analyzed our models' characteristics and properties. The relations between our models for soft fuzzy covering sets and Zhan's model for soft rough fuzzy covering were presented.


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