IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i15p3414-d1211005.html
   My bibliography  Save this article

Expansion Theory of Deng’s Metric in [0,1]-Topology

Author

Listed:
  • Bin Meng

    (Space Star Technology Co., Ltd., Beijing 100095, China)

  • Peng Chen

    (Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China
    University of Chinese Academy of Sciences, Beijing 100049, China)

  • Xiaohui Ba

    (School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China)

Abstract

The aim of this paper is to focus on a fuzzy metric called Deng’s metric in [ 0 , 1 ] -topology. Firstly, we will extend the domain of this metric function from M 0 × M 0 to M × M , where M 0 and M are defined as the sets of all special fuzzy points and all standard fuzzy points, respectively. Secondly, we will further extend this metric to the completely distributive lattice L X and, based on this extension result, we will compare this metric with the other two fuzzy metrics: Erceg’s metric and Yang-Shi’s metric, and then reveal some of its interesting properties, particularly including its quotient space. Thirdly, we will investigate the relationship between Deng’s metric and Yang-Shi’s metric and prove that a Deng’s metric must be a Yang-Shi’s metric on I X , and consequently an Erceg’s metric. Finally, we will show that a Deng’s metric on I X must be Q − C 1 , and Deng’s metric topology and its uniform structure are Erceg’s metric topology and Hutton’s uniform structure, respectively.

Suggested Citation

  • Bin Meng & Peng Chen & Xiaohui Ba, 2023. "Expansion Theory of Deng’s Metric in [0,1]-Topology," Mathematics, MDPI, vol. 11(15), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3414-:d:1211005
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/15/3414/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/15/3414/
    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:11:y:2023:i:15:p:3414-:d:1211005. 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.