Fuzzy Metric Space and Its Topological Properties

Masriani Masriani (Department of Mathematics, Universitas Mataram)
Qurratul Aini (Department of Mathematics, Universitas Mataram)
Syamsul Bahri (Department of Mathematics, Universitas Mataram)

EIGEN MATHEMATICS JOURNAL
Vol. 4 No. 2 Desember 2021

The fuzzy set theory is mathematics that applies fuzziness characteristics, so that gives the truth value at interval [0,1]. It is different from the crisp set that gives a truth value of 0 if it is not a member and 1 if it is a member. The theory of fuzzy sets has been developed continuously by scientists. One of the developments of the fuzzy set is the fuzzy metric space which the definition was introduced by George and Veeramani. Based on the analysis results, it is found that every metric space X if and only if X is fuzzy metric space. As a result, the topological properties of the metric space still apply to the fuzzy metric space