IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i3p252-d212822.html
   My bibliography  Save this article

On ( α , β )-US Sets in BCK / BCI -Algebras

Author

Listed:
  • Chiranjibe Jana

    (Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India)

  • Madhumangal Pal

    (Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India)

Abstract

Molodtsov originated soft set theory, which followed a general mathematical framework for handling uncertainties, in which we encounter the data by affixing the parameterized factor during the information analysis. The aim of this paper is to establish a bridge to connect a soft set and the union operations on sets, then applying it to B C K / B C I -algebras. Firstly, we introduce the notion of the ( α , β ) -Union-Soft ( ( α , β ) -US) set, with some supporting examples. Then, we discuss the soft B C K / B C I -algebras, which are called ( α , β ) -US algebras, ( α , β ) -US ideals, ( α , β ) -US closed ideals, and ( α , β ) -US commutative ideals. In particular, some related properties and relationships of the above algebraic structures are investigated. We also provide the condition of an ( α , β ) -US ideal to be an ( α , β ) -US closed ideal. Some conditions for a Union-Soft (US) ideal to be a US commutative ideal are given by means of ( α , β ) -unions. Moreover, several characterization theorems of (closed) US ideals and US commutative ideals are given in terms of ( α , β ) -unions. Finally, the extension property for an ( α , β ) -US commutative ideal is established.

Suggested Citation

  • Chiranjibe Jana & Madhumangal Pal, 2019. "On ( α , β )-US Sets in BCK / BCI -Algebras," Mathematics, MDPI, vol. 7(3), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:252-:d:212822
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/3/252/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/3/252/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Çagman, Naim & Enginoglu, Serdar, 2010. "Soft set theory and uni-int decision making," European Journal of Operational Research, Elsevier, vol. 207(2), pages 848-855, December.
    Full references (including those not matched with items on IDEAS)

    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. Raees Khan & Asghar Khan & M. Uzair Khan & Hidayat Ullah Khan, 2018. "Right Pure Uni-Soft Ideals Of Ordered Semigroups," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 2(1), pages 18-23, January.
    2. 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.
    3. Yong Yang & Ling Zeng & Xia Tan & Hao Chen, 2013. "Similarity coefficient in soft set theory," Fuzzy Information and Engineering, Springer, vol. 5(1), pages 119-126, March.
    4. 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.
    5. Santanu Acharjee, 2018. "On Connections of Soft Set Theory with Existing Mathematics of Uncertainties: A Short Discussion for Non-Mathematicians with Respect to Soft Set Theory," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-9, March.

    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:7:y:2019:i:3:p:252-:d:212822. 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.