Syarat Perlu atau Cukup F-bounded di dalam Ruang Metrik-α Fuzzy

Lukman Zicky, Mahmud Yunus


Metrics have an important role in mathematics, both in analysis as well as applications. One of the new concepts of metric space is fuzzy -metric space. This metric space is an expansion of the fuzzy metric space by adding  generator. In this paper, we discuss characterization of F-bounded in the fuzzy -metric space. The property of F-bounded is obtained from the compact subset of a given universe set. This characteristic has been discussed by Changqing and Kedian in Hausdorff fuzzy metric spaces. In this paper, the necessary and sufficient conditions are obtained so that the fuzzy  -metric space satisfies the properties of F-bounded.


fuzzy α-metric space; α generator; F-bounded

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Cevik, C., & Eminoglu, S. (2018). Generated Fuzzy Metric Space and Some Topological Properties. Intelligent & Fuzzy Systems, 877-885.

Changqing, L., & Kedian, L. (2017). On Topological Properties of the Hausdorff Fuzzy Metric Spaces. Filomat, 1167-1173.

George, A., & Veeramani, P. (1994). On Some Results in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 395-399.

Gomez, S. (2007). Fuzzy Metrics and Fuzzy Logic for Colour Image Filtering. Valencia: Universidad de Politecnica.

Kramosil, I., & Michalek, J. (1975). Fuzzy Metric and Statistical Metric. 326-334.

Kreyzig, E. (1978). Introductory Functional Analysis with Appliations. Canada: John Wiley & Sons.

Kumam, P., & Wuthipol, S. (2011). Common Fixed Theorems for a Pair of Weakly Compatible Mapping in Fuzzy Metric Spaces. Hindawi, 1-14.

Lukman, Z. (2018). Fixed Point Theorem on Fuzzy Metric Spaces. Surabaya: Mathematic department of ITS.

Missier, S. P., & Rodrigo, P. A. (2014). Strongly alpha Countinuous Functions in Topological Spaces. IOSR Journal of Mathematics, 55-60.

Zadeh, A. L. (1965). Fuzzy Sets. Inform and Control, 338-353.

Zimmerman. (1992). Fuzzy Sets and Its Applications. Massachusetts: Kluwer Academic Publisher.



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