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

Bin Meng, Peng Chen () and Xiaohui Ba
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Bin Meng: Space Star Technology Co., Ltd., Beijing 100095, China
Peng Chen: Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China
Xiaohui Ba: School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China

Mathematics, 2023, vol. 11, issue 15, 1-17

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.

Keywords: Deng’s pseudo-metric; expansion; M 0; M; metric topology; way below; Q ? C 1 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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