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The Relationship between Ordinary and Soft Algebras with an Application

Author

Listed:
  • Zanyar A. Ameen

    (Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq)

  • Tareq M. Al-shami

    (Department of Mathematics, Sana’a University, Sana’a P.O. Box 1247, Yemen
    Department of Engineering Mathematics & Physics, Faculty of Engineering & Technology, Future University, Cairo 11835, Egypt)

  • Radwan Abu-Gdairi

    (Department of Mathematics, Faculty of Science, Zarqa University, Zarqa P.O. Box 13110, Jordan)

  • Abdelwaheb Mhemdi

    (Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh 16273, Saudi Arabia)

Abstract

This work makes a contribution to the theory of soft sets. It studies the concepts of soft semi-algebras and soft algebras, along with some operations. Then, it examines the relations of soft algebras set to their ordinary (crisp) counterparts. Among other things, we show that every algebra of soft sets induces a collection of ordinary algebras of sets. By using the formulas (in Theorem 7 and Corollary 1), we present a novel construction, allowing us to construct a soft algebra from a system of ordinary algebras of sets. Two examples are presented to show how these formulas can be used in practice. This approach is general enough to be applied to many other (soft) algebraic properties and shows that ordinary algebras contain instruments enabling us to construct soft algebras and to study their properties. As an application, we demonstrate how elements of the generated soft algebra can be used to describe the weather conditions of a region.

Suggested Citation

  • Zanyar A. Ameen & Tareq M. Al-shami & Radwan Abu-Gdairi & Abdelwaheb Mhemdi, 2023. "The Relationship between Ordinary and Soft Algebras with an Application," Mathematics, MDPI, vol. 11(9), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2035-:d:1132452
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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. Tareq M. Al-shami, 2021. "New Soft Structure: Infra Soft Topological Spaces," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-12, July.
    3. Tareq M. Al-shami & Abdelwaheb Mhemdi & Radwan Abu-Gdairi, 2023. "A Novel Framework for Generalizations of Soft Open Sets and Its Applications via Soft Topologies," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    4. Tareq M. Al-shami & Abdelwaheb Mhemdi & Sami Ullah Khan, 2021. "Belong and Nonbelong Relations on Double-Framed Soft Sets and Their Applications," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, May.
    5. Tareq M. Al-shami & Ahmed Mostafa Khalil, 2021. "Bipolar Soft Sets: Relations between Them and Ordinary Points and Their Applications," Complexity, Hindawi, vol. 2021, pages 1-14, January.
    6. T. M. Al-shami & Ching-Feng Wen, 2021. "Compactness on Soft Topological Ordered Spaces and Its Application on the Information System," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, January.
    7. Athar Kharal & B. Ahmad, 2011. "Mappings On Soft Classes," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 471-481.
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    Cited by:

    1. Ahmad Al-Omari & Wafa Alqurashi, 2023. "Hyperconnectedness and Resolvability of Soft Ideal Topological Spaces," Mathematics, MDPI, vol. 11(22), pages 1-10, November.
    2. Sandeep Kaur & Tareq M. Al-shami & Alkan Özkan & M. Hosny, 2023. "A New Approach to Soft Continuity," Mathematics, MDPI, vol. 11(14), pages 1-11, July.
    3. Zanyar A. Ameen & Mesfer H. Alqahtani, 2023. "Some Classes of Soft Functions Defined by Soft Open Sets Modulo Soft Sets of the First Category," Mathematics, MDPI, vol. 11(20), pages 1-15, October.

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