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

Peng Chen (), Bin Meng and Xiaohui Ba
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Peng Chen: Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, 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

Mathematics, 2023, vol. 11, issue 14, 1-15

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.

Keywords: L -quasi (pseudo)-metric; co-prime element; irreducible element; way below; R-neighborhood; T 1 -space; Q ? C I (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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