IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i14p2429-d860948.html
   My bibliography  Save this article

Regular Partial Residuated Lattices and Their Filters

Author

Listed:
  • Nan Sheng

    (School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China)

  • Xiaohong Zhang

    (School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China)

Abstract

To express wider uncertainty, Běhounek and Daňková studied fuzzy partial logic and partial function. At the same time, Borzooei generalized t-norms and put forward the concept of partial t-norms when studying lattice valued quantum effect algebras. Based on partial t-norms, Zhang et al. studied partial residuated implications (PRIs) and proposed the concept of partial residuated lattices (PRLs). In this paper, we mainly study the related algebraic structure of fuzzy partial logic. First, we provide the definitions of regular partial t-norms and regular partial residuated implication (rPRI) through the general forms of partial t-norms and partial residuated implication. Second, we define regular partial residuated lattices (rPRLs) and study their corresponding properties. Third, we study the relations among commutative quasi-residuated lattices, commutative Q-residuated lattices, partial residuated lattices, and regular partial residuated lattices. Last, in order to obtain the filter theory of regular partial residuated lattices, we restrict certain conditions and then propose special regular partial residuated lattices (srPRLs) in order to finally construct the quotient structure of regular partial residuated lattices.

Suggested Citation

  • Nan Sheng & Xiaohong Zhang, 2022. "Regular Partial Residuated Lattices and Their Filters," Mathematics, MDPI, vol. 10(14), pages 1-16, July.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2429-:d:860948
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/14/2429/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/14/2429/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xiaohong Zhang & Yudan Du, 2022. "Left (Right) Regular and Transposition Regular Semigroups and Their Structures," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
    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. Mingdi Hu & Chenrui Wang & Jingbing Yang & Yi Wu & Jiulun Fan & Bingyi Jing, 2022. "Rain Rendering and Construction of Rain Vehicle Color -24 Dataset," Mathematics, MDPI, vol. 10(17), pages 1-18, September.
    2. Rong Liang & Xiaohong Zhang, 2022. "Pseudo General Overlap Functions and Weak Inflationary Pseudo BL-Algebras," Mathematics, MDPI, vol. 10(16), pages 1-15, August.
    3. Mingdi Hu & Yixuan Li & Jiulun Fan & Bingyi Jing, 2022. "Joint Semantic Deep Learning Algorithm for Object Detection under Foggy Road Conditions," Mathematics, MDPI, vol. 10(23), pages 1-17, November.
    4. Mingdi Hu & Yi Wu & Jiulun Fan & Bingyi Jing, 2022. "Joint Semantic Intelligent Detection of Vehicle Color under Rainy Conditions," Mathematics, MDPI, vol. 10(19), pages 1-16, September.
    5. Xiaohong Zhang & Rong Liang & Benjamín Bedregal, 2022. "Weak Inflationary BL-Algebras and Filters of Inflationary (Pseudo) General Residuated Lattices," Mathematics, MDPI, vol. 10(18), pages 1-21, September.

    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.

      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:14:p:2429-:d:860948. 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.