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Stronger Forms of Fuzzy Pre-Separation and Regularity Axioms via Fuzzy Topology

Author

Listed:
  • Salem Saleh

    (Department of Computer Science, Cihan University-Erbil, Erbil P.O. Box 44001, Iraq
    Department of Mathematics, Hodeidah University, Hodeidah P.O. Box 3114, Yemen)

  • Tareq M. Al-shami

    (Department of Mathematics, Sana’a University, Sana’a P.O. Box 1247, Yemen)

  • A. A. Azzam

    (Department of Mathematics, Faculty of Science and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
    Department of Mathematics, Faculty of Science, New Valley University, Elkharga 72511, Egypt)

  • M. Hosny

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

Abstract

It is common knowledge that fuzzy topology contributes to developing techniques to address real-life applications in various areas like information systems and optimal choices. The building blocks of fuzzy topology are fuzzy open sets, but other extended families of fuzzy open sets, like fuzzy pre-open sets, can contribute to the growth of fuzzy topology. In the present work, we create some classifications of fuzzy topologies which enable us to obtain several desirable features and relationships. At first, we introduce and analyze stronger forms of fuzzy pre-separation and regularity properties in fuzzy topology called fuzzy pre- T i , i = 0 , 1 2 , 1 , 2 , 3 , 4 , fuzzy pre-symmetric, and fuzzy pre- R i , i = 0 , 1 , 2 , 3 by utilizing the concepts of fuzzy pre-open sets and quasi-coincident relation. We investigate more novel properties of these classes and uncover their unique characteristics. By presenting a wide array of related theorems and interconnections, we structure a comprehensive framework for understanding these classes and interrelationships with other separation axioms in this setting. Moreover, the relations between these classes and those in some induced topological structures are examined. Additionally, we explore the hereditary and harmonic properties of these classes.

Suggested Citation

  • Salem Saleh & Tareq M. Al-shami & A. A. Azzam & M. Hosny, 2023. "Stronger Forms of Fuzzy Pre-Separation and Regularity Axioms via Fuzzy Topology," Mathematics, MDPI, vol. 11(23), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4801-:d:1289390
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    References listed on IDEAS

    as
    1. Tareq M. Al-shami & José Carlos R. Alcantud & A. A. Azzam, 2022. "Two New Families of Supra-Soft Topological Spaces Defined by Separation Axioms," Mathematics, MDPI, vol. 10(23), pages 1-18, November.
    2. M. E. El-Shafei & A. H. Zakari & T. M. Al-shami & Ljubisa Kocinac, 2020. "Some Applications of Supra Preopen Sets," Journal of Mathematics, Hindawi, vol. 2020, pages 1-11, May.
    3. Weidong Tang & Jinzhao Wu & Dingwei Zheng, 2014. "On Fuzzy Rough Sets and Their Topological Structures," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-17, January.
    Full references (including those not matched with items on IDEAS)

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