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L -Quasi (Pseudo)-Metric in L -Fuzzy Set Theory

Author

Listed:
  • Peng Chen

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

  • Bin Meng

    (Space Star Technology Co., Ltd., Beijing 100095, 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 the metrization question in L -fuzzy sets. Firstly, we put forward an L -quasi (pseudo)-metric on the completely distributive lattice L X by comparing some existing lattice-valued metrics with the classical metric and show a series of its related properties. Secondly, we present two topologies: ψ p and ζ p , generated by an L -quasi-metric p with different spherical mappings, and prove ψ p = ζ p ′ if p is further an L -pseudo-metric on L X . Thirdly, we characterize an equivalent form of L -pseudo-metric in terms of a class of mapping clusters and acquire several satisfactory results. Finally, based on this kind of L -metric, we assert that, on L X , a Yang–Shi metric topology is Q − C I , but an Erceg metric topology is not always so.

Suggested Citation

  • Peng Chen & Bin Meng & Xiaohui Ba, 2023. "L -Quasi (Pseudo)-Metric in L -Fuzzy Set Theory," Mathematics, MDPI, vol. 11(14), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3152-:d:1196573
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