# Fuzzy b-Metric Spaces

### Abstract

Metric spaces and their various generalizations occur frequently in computer science applications. This is the reason why, in this paper, we introduced and studied the concept of fuzzy b-metric space, generalizing, in this way, both the notion of fuzzy metric space introduced by I. Kramosil and J. Michálek and the concept of b-metric space. On the other hand, we introduced the concept of fuzzy quasi-bmetric space, extending the notion of fuzzy quasi metric space recently introduced by V. Gregori and S. Romaguera. Finally, a decomposition theorem for a fuzzy quasipseudo- b-metric into an ascending family of quasi-pseudo-b-metrics is established. The use of fuzzy b-metric spaces and fuzzy quasi-b-metric spaces in the study of denotational semantics and their applications in control theory will be an important next step.### References

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**INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL**, [S.l.], v. 11, n. 2, p. 273-281, jan. 2016. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/2443>. Date accessed: 02 july 2020. doi: https://doi.org/10.15837/ijccc.2016.2.2443.

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