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

Yu Zhong, Xin Wu, Alexander Šostak and Fu-Gui Shi
Additional contact information
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

Mathematics, 2022, vol. 10, issue 7, 1-17

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.

Keywords: ( L , M )-fuzzy k-pseudo metric; ( L , M )-fuzzy k-remote neighborhood ball system; ( L , M )-fuzzy topology; ( L , M )-fuzzy quasi-neighborhood system; nest of pointwise k-pseudo metrics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/7/1151/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/7/1151/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:7:p:1151-:d:786132

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().