IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i13p2274-d851273.html
   My bibliography  Save this article

Rough Semiring-Valued Fuzzy Sets with Application

Author

Listed:
  • Jiří Močkoř

    (Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. Dubna 22, 702 00 Ostrava, Czech Republic)

  • Petr Hurtik

    (Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. Dubna 22, 702 00 Ostrava, Czech Republic)

  • David Hýnar

    (Varroc Lighting Systems, Suvorovova 195, 742 42 Šenov u Nového Jičína, Czech Republic)

Abstract

Many of the new fuzzy structures with complete M V -algebras as value sets, such as hesitant, intuitionistic, neutrosophic, or fuzzy soft sets, can be transformed into one type of fuzzy set with values in special complete algebras, called A M V -algebras. The category of complete A M V -algebras is isomorphic to the category of special pairs ( R , R ∗ ) of complete commutative semirings and the corresponding fuzzy sets are called ( R , R ∗ ) -fuzzy sets. We use this theory to define ( R , R ∗ ) -fuzzy relations, lower and upper approximations of ( R , R ∗ ) -fuzzy sets by ( R , R ∗ ) -relations, and rough ( R , R ∗ ) -fuzzy sets, and we show that these notions can be universally applied to any fuzzy type structure that is transformable to ( R , R ∗ ) -fuzzy sets. As an example, we also show how this general theory can be used to determine the upper and lower approximations of a color segment corresponding to a particular color.

Suggested Citation

  • Jiří Močkoř & Petr Hurtik & David Hýnar, 2022. "Rough Semiring-Valued Fuzzy Sets with Application," Mathematics, MDPI, vol. 10(13), pages 1-31, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2274-:d:851273
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/13/2274/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/13/2274/
    Download Restriction: no
    ---><---

    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:10:y:2022:i:13:p:2274-:d:851273. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.