Pointwise (L, M)-fuzzy uniformities induced by (L, M)-fuzzy pseudo-metric and pointwise pseudo-metric chains

Xiu Yun Wu; Bin Pang; Zhen Yu Xiu

doi:10.3233/JIFS-152492

Pointwise (L, M)-fuzzy uniformities induced by (L, M)-fuzzy pseudo-metric and pointwise pseudo-metric chains

Xiu Yun Wu, Bin Pang, Zhen Yu Xiu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, the relations among (L, M)-fuzzy pseudo-metrics, pointwise pseudo-metric chains and pointwise (L, M)-fuzzy uniformities are investigated. It is shown that an (L, M)-fuzzy pseudo-metric can induce a pointwise (L, M)-fuzzy uniformity, and an (L, M)-fuzzy pseudo-metric and its induced pointwise (L, M)-fuzzy uniformity generate the same (L, M)-fuzzy topology. Also, it is proved that a pointwise pseudo-metric chain can induce a pointwise (L, M)-fuzzy uniformity, and a pointwise pseudo-metric chain and its induced (L, M)-fuzzy pseudo-metric generate the same pointwise (L, M)-fuzzy uniformity. Moreover, a pointwise pseudo-metric chain and its induced pointwise (L, M)-fuzzy uniformity generate the same (L, M)-fuzzy topology.

Original language	English
Pages (from-to)	579-588
Number of pages	10
Journal	Journal of Intelligent and Fuzzy Systems
Volume	35
Issue number	1
DOIs	https://doi.org/10.3233/JIFS-152492
Publication status	Published - 2018

Keywords

(L, M)-fuzzy pseudo-metric
(L, M)-fuzzy topology
Pointwise (L, M)-fuzzy uniformity
Pointwise pseudo-metric chain

Access to Document

10.3233/JIFS-152492

Cite this

@article{c14961d5d1fe4a5cb1cf2f47c16c91f8,

title = "Pointwise (L, M)-fuzzy uniformities induced by (L, M)-fuzzy pseudo-metric and pointwise pseudo-metric chains",

abstract = "In this paper, the relations among (L, M)-fuzzy pseudo-metrics, pointwise pseudo-metric chains and pointwise (L, M)-fuzzy uniformities are investigated. It is shown that an (L, M)-fuzzy pseudo-metric can induce a pointwise (L, M)-fuzzy uniformity, and an (L, M)-fuzzy pseudo-metric and its induced pointwise (L, M)-fuzzy uniformity generate the same (L, M)-fuzzy topology. Also, it is proved that a pointwise pseudo-metric chain can induce a pointwise (L, M)-fuzzy uniformity, and a pointwise pseudo-metric chain and its induced (L, M)-fuzzy pseudo-metric generate the same pointwise (L, M)-fuzzy uniformity. Moreover, a pointwise pseudo-metric chain and its induced pointwise (L, M)-fuzzy uniformity generate the same (L, M)-fuzzy topology.",

keywords = "(L, M)-fuzzy pseudo-metric, (L, M)-fuzzy topology, Pointwise (L, M)-fuzzy uniformity, Pointwise pseudo-metric chain",

author = "Wu, {Xiu Yun} and Bin Pang and Xiu, {Zhen Yu}",

note = "Publisher Copyright: {\textcopyright} 2018 - IOS Press and the authors.",

year = "2018",

doi = "10.3233/JIFS-152492",

language = "English",

volume = "35",

pages = "579--588",

journal = "Journal of Intelligent and Fuzzy Systems",

issn = "1064-1246",

publisher = "IOS Press BV",

number = "1",

}

TY - JOUR

T1 - Pointwise (L, M)-fuzzy uniformities induced by (L, M)-fuzzy pseudo-metric and pointwise pseudo-metric chains

AU - Wu, Xiu Yun

AU - Pang, Bin

AU - Xiu, Zhen Yu

PY - 2018

Y1 - 2018

N2 - In this paper, the relations among (L, M)-fuzzy pseudo-metrics, pointwise pseudo-metric chains and pointwise (L, M)-fuzzy uniformities are investigated. It is shown that an (L, M)-fuzzy pseudo-metric can induce a pointwise (L, M)-fuzzy uniformity, and an (L, M)-fuzzy pseudo-metric and its induced pointwise (L, M)-fuzzy uniformity generate the same (L, M)-fuzzy topology. Also, it is proved that a pointwise pseudo-metric chain can induce a pointwise (L, M)-fuzzy uniformity, and a pointwise pseudo-metric chain and its induced (L, M)-fuzzy pseudo-metric generate the same pointwise (L, M)-fuzzy uniformity. Moreover, a pointwise pseudo-metric chain and its induced pointwise (L, M)-fuzzy uniformity generate the same (L, M)-fuzzy topology.

AB - In this paper, the relations among (L, M)-fuzzy pseudo-metrics, pointwise pseudo-metric chains and pointwise (L, M)-fuzzy uniformities are investigated. It is shown that an (L, M)-fuzzy pseudo-metric can induce a pointwise (L, M)-fuzzy uniformity, and an (L, M)-fuzzy pseudo-metric and its induced pointwise (L, M)-fuzzy uniformity generate the same (L, M)-fuzzy topology. Also, it is proved that a pointwise pseudo-metric chain can induce a pointwise (L, M)-fuzzy uniformity, and a pointwise pseudo-metric chain and its induced (L, M)-fuzzy pseudo-metric generate the same pointwise (L, M)-fuzzy uniformity. Moreover, a pointwise pseudo-metric chain and its induced pointwise (L, M)-fuzzy uniformity generate the same (L, M)-fuzzy topology.

KW - (L, M)-fuzzy pseudo-metric

KW - (L, M)-fuzzy topology

KW - Pointwise (L, M)-fuzzy uniformity

KW - Pointwise pseudo-metric chain

UR - http://www.scopus.com/inward/record.url?scp=85051370038&partnerID=8YFLogxK

U2 - 10.3233/JIFS-152492

DO - 10.3233/JIFS-152492

M3 - Article

AN - SCOPUS:85051370038

SN - 1064-1246

VL - 35

SP - 579

EP - 588

JO - Journal of Intelligent and Fuzzy Systems

JF - Journal of Intelligent and Fuzzy Systems

IS - 1

ER -

Pointwise (L, M)-fuzzy uniformities induced by (L, M)-fuzzy pseudo-metric and pointwise pseudo-metric chains

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this