Uniformities in fuzzy metric spaces

The aim of this paper is to study induced (quasi-)uniformities in Kramosil and Michalek's fuzzy metric spaces. Firstly, I-uniformity in the sense of J. Guti'{e}rrez  Garc'{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.

کلیدواژه ها:

Fuzzy metric ، I-uniformity ، Hutton quasi-uniformity