Some Remarks on Fuzzy sb -Metric Spaces

Tarkan Öner and Alexander Šostak
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Tarkan Öner: Department of Mathematics, Muğla Sıtkı Koçman University, Muğla 48000, Turkey
Alexander Šostak: Institute of Mathematics and CS and Department of Mathematics, University of Latvia, LV-1586 Riga, Latvia

Mathematics, 2020, vol. 8, issue 12, 1-19

Abstract: Fuzzy strong b -metrics called here by fuzzy sb-metrics, were introduced recently as a fuzzy version of strong b -metrics. It was shown that open balls in fuzzy s b -metric spaces are open in the induced topology (as different from the case of fuzzy b -metric spaces) and thanks to this fact fuzzy s b -metrics have many useful properties common with fuzzy metric spaces which generally may fail to be in the case of fuzzy b -metric spaces. In the present paper, we go further in the research of fuzzy s b -metric spaces. It is shown that the class of fuzzy s b -metric spaces lies strictly between the classes of fuzzy metric and fuzzy b -metric spaces. We prove that the topology induced by a fuzzy s b -metric is metrizable. A characterization of completeness in terms of diameter zero sets in these structures is given. We investigate products and coproducts in the naturally defined category of fuzzy s b -metric spaces.

Keywords: fuzzy metric; fuzzy sb -metric; fuzzy b -metric (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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