IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i9p2035-d1132452.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/9/2035/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/9/2035/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tareq M. Al-shami & Zanyar A. Ameen & Radwan Abu-Gdairi & Abdelwaheb Mhemdi, 2023. "On Primal Soft Topology," Mathematics, MDPI, vol. 11(10), pages 1-15, May.
    2. 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.
    3. Tareq M. Al-shami & El-Sayed A. Abo-Tabl, 2021. "Connectedness and Local Connectedness on Infra Soft Topological Spaces," Mathematics, MDPI, vol. 9(15), pages 1-13, July.
    4. 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.
    5. Samer Al Ghour, 2021. "Soft Semi ω -Open Sets," Mathematics, MDPI, vol. 9(24), pages 1-12, December.
    6. Ahmad Al-Omari & Wafa Alqurashi, 2023. "Hyperconnectedness and Resolvability of Soft Ideal Topological Spaces," Mathematics, MDPI, vol. 11(22), pages 1-10, November.
    7. Sagvan Y. Musa & Baravan A. Asaad, 2021. "Bipolar Hypersoft Sets," Mathematics, MDPI, vol. 9(15), pages 1-15, August.
    8. Samer Al Ghour & Hanan Al-Saadi, 2023. "Soft ω - θ -Continuous and Soft Weakly θ ω -Continuous Mappings," Mathematics, MDPI, vol. 11(19), pages 1-15, September.
    9. José Carlos R. Alcantud & Tareq M. Al-shami & A. A. Azzam, 2021. "Caliber and Chain Conditions in Soft Topologies," Mathematics, MDPI, vol. 9(19), pages 1-15, September.
    10. Dina Abuzaid & Samer Al-Ghour & Monia Naghi, 2024. "On Soft ω δ -Open Sets and Some Decomposition Theorems," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    11. Samer Al Ghour, 2021. "Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    12. Apostolos G. Christopoulos & Ioannis G. Dokas & Iraklis Kollias & John Leventides, 2019. "An implementation of Soft Set Theory in the Variables Selection Process for Corporate Failure Prediction Models. Evidence from NASDAQ Listed Firms," Bulletin of Applied Economics, Risk Market Journals, vol. 6(1), pages 1-20.
    13. 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.
    14. Muhammad Saeed & Muhammad Ahsan & Muhammad Haris Saeed & Atiqe Ur Rahman & Asad Mehmood & Mazin Abed Mohammed & Mustafa Musa Jaber & Robertas Damaševičius, 2022. "An Optimized Decision Support Model for COVID-19 Diagnostics Based on Complex Fuzzy Hypersoft Mapping," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    15. Samer Al Ghour & Hanan Al-Saadi, 2023. "Soft Slight Omega-Continuity and Soft Ultra-Separation Axioms," Mathematics, MDPI, vol. 11(15), pages 1-17, July.
    16. Arif Mehmood Khattak & Gulzar Ali Khan & Younis Khan & Muhammad Ishfaq Khattak & Fahad Jamal, 2018. "Characterization Of Soft B Separation Axioms In Soft Bi-Topological Spaces," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 2(2), pages 11-17, January.
    17. Samajh Singh Thakur & Alpa Singh Rajput, 2018. "Connectedness Between Soft Sets," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 53-71, March.
    18. Tahir Ayaz & Arif Mehmood Khattak & Nisar Ahmad, 2018. "Supra Soft R-Separation Axioms," Acta Scientifica Malaysia (ASM), Zibeline International Publishing, vol. 2(2), pages 27-31, August.
    19. H. Hazra & P. Majumdar & S. K. Samanta, 2012. "Soft topology," Fuzzy Information and Engineering, Springer, vol. 4(1), pages 105-115, March.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2035-:d:1132452. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.