Some Properties of Partial Fuzzy Metric Topology

Aydoğdu, Ebru; Aldemir, Başak; Güner, Elif; Aygün, Halis

doi:10.1007/978-3-030-51156-2_148

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2022

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Cited by 2 publications

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“…The other one is the concept of partial fuzzy metric spaces was given by Sedghi et al [27] who generalizes the structure of strong GV-fuzzy metric spaces. Some fundamental fixed point theorems and topological properties can be found in [1,3]. Another approach to partial metric space in the fuzzy settings by using the residuum operator was given by Gregori et al [10].…”

Section: Introductionmentioning

confidence: 99%

A new approach to fuzzy partial metric spaces

Güner

Aygün

2022

Hacettepe Journal of Mathematics and Statistics

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In this study, we aim to introduce the notion of fuzzy partial metric spaces which is a generalization of crisp partial metric spaces in the fuzzifying view with the distance between ordinary points. For this aim, we first present the concept of fuzzy partial metric spaces by considering the distance as non-negative, upper semi-continuous, normal and convex fuzzy numbers by giving examples. We obtain some useful inequalities under some restrictions in fuzzy partial metric spaces. Then we discuss the relationships with the other metric structures and we point out Banach's fixed point theorem as an application of the proposed properties and relations. Finally, we show that fuzzy partial metric spaces induce some $\alpha$-level topology, Lowen fuzzy topology, and fuzzifying topology.

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Section: Introductionmentioning

confidence: 99%