A new approach for KM-fuzzy partial metric spaces

Yu Shen; Chong Shen; Conghua Yan

Kybernetika (2022)

  • Volume: 58, Issue: 1, page 64-81
  • ISSN: 0023-5954

Abstract

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The main purpose of this paper is to give a new approach for partial metric spaces. We first provide the new concept of KM-fuzzy partial metric, as an extension of both the partial metric and KM-fuzzy metric. Then its relationship with the KM-fuzzy quasi-metric is established. In particularly, we construct a KM-fuzzy quasi-metric from a KM-fuzzy partial metric. Finally, after defining the notion of partial pseudo-metric systems, a one-to-one correspondence between partial pseudo-metric systems and KM-fuzzy partial pseudo-metrics is constructed. Furthermore, a fuzzifying topology τ P on X deduced from KM-fuzzy partial metric is established and some properties of this fuzzifying topology are discussed.

How to cite

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Shen, Yu, Shen, Chong, and Yan, Conghua. "A new approach for KM-fuzzy partial metric spaces." Kybernetika 58.1 (2022): 64-81. <http://eudml.org/doc/297421>.

@article{Shen2022,
abstract = {The main purpose of this paper is to give a new approach for partial metric spaces. We first provide the new concept of KM-fuzzy partial metric, as an extension of both the partial metric and KM-fuzzy metric. Then its relationship with the KM-fuzzy quasi-metric is established. In particularly, we construct a KM-fuzzy quasi-metric from a KM-fuzzy partial metric. Finally, after defining the notion of partial pseudo-metric systems, a one-to-one correspondence between partial pseudo-metric systems and KM-fuzzy partial pseudo-metrics is constructed. Furthermore, a fuzzifying topology $\tau _\{P\}$ on X deduced from KM-fuzzy partial metric is established and some properties of this fuzzifying topology are discussed.},
author = {Shen, Yu, Shen, Chong, Yan, Conghua},
journal = {Kybernetika},
keywords = {partial metric; KM-fuzzy metric; KM-fuzzy partial metric; partial pseudo-metric system; fuzzy neighborhood system},
language = {eng},
number = {1},
pages = {64-81},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A new approach for KM-fuzzy partial metric spaces},
url = {http://eudml.org/doc/297421},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Shen, Yu
AU - Shen, Chong
AU - Yan, Conghua
TI - A new approach for KM-fuzzy partial metric spaces
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 1
SP - 64
EP - 81
AB - The main purpose of this paper is to give a new approach for partial metric spaces. We first provide the new concept of KM-fuzzy partial metric, as an extension of both the partial metric and KM-fuzzy metric. Then its relationship with the KM-fuzzy quasi-metric is established. In particularly, we construct a KM-fuzzy quasi-metric from a KM-fuzzy partial metric. Finally, after defining the notion of partial pseudo-metric systems, a one-to-one correspondence between partial pseudo-metric systems and KM-fuzzy partial pseudo-metrics is constructed. Furthermore, a fuzzifying topology $\tau _{P}$ on X deduced from KM-fuzzy partial metric is established and some properties of this fuzzifying topology are discussed.
LA - eng
KW - partial metric; KM-fuzzy metric; KM-fuzzy partial metric; partial pseudo-metric system; fuzzy neighborhood system
UR - http://eudml.org/doc/297421
ER -

References

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