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Uniformities in fuzzy metric spaces | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 4، دوره 12، شماره 1، اردیبهشت 2015، صفحه 43-57 اصل مقاله (456.86 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2015.1841 | ||
| نویسندگان | ||
| Yueli Yue* ؛ Jinming Fang | ||
| Department of Mathematics, Ocean University of China, 238 Songling Road, 266100, Qingdao, P.R.China | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Fuzzy metric؛ $I$-uniformity؛ Hutton quasi-uniformity | ||
| مراجع | ||
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