University of Sistan and BaluchestanIranian Journal of Fuzzy Systems1735-065412120150228Uniformities in fuzzy metric spaces4357184110.22111/ijfs.2015.1841ENYueliYueDepartment of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.ChinaJinmingFangDepartment of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.ChinaJournal Article20131208The 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}rrezĀ 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.https://ijfs.usb.ac.ir/article_1841_934512989c8d6bed65891801d995c6a2.pdf