Geodesic
A new approach for KM-fuzzy partial metric spaces
Kybernetika, Tome 58 (2022) no. 1, pp. 64-81
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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 $\tau_{P}$ on X deduced from KM-fuzzy partial metric is established and some properties of this fuzzifying topology are discussed.
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.
DOI : 10.14736/kyb-2022-1-0064
Classification : 46S40, 54A40
Keywords: partial metric; KM-fuzzy metric; KM-fuzzy partial metric; partial pseudo-metric system; fuzzy neighborhood system 
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Shen, Yu; Shen, Chong; Yan, Conghua. A new approach for KM-fuzzy partial metric spaces. Kybernetika, Tome 58 (2022) no. 1, pp. 64-81. doi: 10.14736/kyb-2022-1-0064

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