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( L , M )-Fuzzy k -Pseudo Metric Space

Author

Listed:
  • Yu Zhong

    (College of Science, North China University of Technology, Beijing 100144, China)

  • Xin Wu

    (College of Science, North China University of Technology, Beijing 100144, China)

  • Alexander Šostak

    (Institute of Mathematics and Computer Science, University of Latvia, LV-1459 Riga, Latvia)

  • Fu-Gui Shi

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, China)

Abstract

Recently, the notion of a classical k -metric, which make the triangle inequality to a more general axiom: d ( x , z ) ≤ k ( d ( x , y ) + d ( y , z ) ) , has been presented and is applied in many fields. In this paper, the definitions of an ( L , M ) -fuzzy k -pseudo metric and an ( L , M ) -fuzzy k -remote neighborhood ball system are introduced. It is proved that the category of ( L , M ) -fuzzy k -pseudo metric spaces is isomorphic to the category of ( L , M ) -fuzzy k -remote neighborhood ball spaces. Besides, ( L , M ) -fuzzy topological structures induced by an ( L , M ) -fuzzy k -pseudo metric are presented and their properties are investigated. Finally, the concept of a nest of pointwise k -pseudo metrics is proposed and it is shown that there is a one-to-one correspondence between ( L , M ) -fuzzy k -pseudo metrics and nests of pointwise k -pseudo metrics.

Suggested Citation

  • Yu Zhong & Xin Wu & Alexander Šostak & Fu-Gui Shi, 2022. "( L , M )-Fuzzy k -Pseudo Metric Space," Mathematics, MDPI, vol. 10(7), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1151-:d:786132
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    References listed on IDEAS

    as
    1. Fu-Gui Shi & Zhen-Yu Xiu, 2014. "A New Approach to the Fuzzification of Convex Structures," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-12, August.
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