Kybernetika 58 no. 1, 64-81, 2022

A new approach for KM-fuzzy partial metric spaces

Yu Shen, Chong Shen and Conghua YanDOI: 10.14736/kyb-2022-1-0064

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.

Keywords:

partial metric, KM-fuzzy metric, KM-fuzzy partial metric, partial pseudo-metric system, fuzzy neighborhood system

Classification:

54A40, 46S40

paper.pdf

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