Uniformities in fuzzy metric spaces

The aim of this paper is to study induced (quasi-)uniformities in Kramosil and Michalekʹs fuzzy metric spaces. Firstly, $I$-uniformity in the sense of J. Guti\ʹ{e}rrez Garc\ʹ{i}a and $I$-neighborhood system in the sense of H\"{o}hle and \u{S}ostak are induced by the given fuzzy metric. It is shown that the fuzzy metric and the induced $I$-uniformity will generate the same $I$-neighborhood system. Secondly, the relationship between Hutton quasi-uniformities and $I$-quasi-uniformities is given and it is proved that the category of strongly stratified $I$-quasi-uniform spaces can be embedded in the category of Hutton quasi-uniform spaces as a bicoreflective subcategory. Also it is shown that two kinds of Hutton quasi-uniformities can generate the same $I$-uniformity in fuzzy metric spaces.