کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
391060 | 661336 | 2007 | 14 صفحه PDF | دانلود رایگان |
An (L,M)-fuzzy topology is a graded extension of topological spaces handling M-valued families of L-fuzzy subsets of a referential, where L and M are completely distributive lattices. When M reduces to the set 2={0,1}, a (2,M)-fuzzy topology is called a fuzzifying topology after Ying. Šostak introduced the notion (L,M)-fuzzy uniform spaces. The aim of this paper is to study the relationship between (2,M)-fuzzy quasi-uniform spaces and (L,M)-fuzzy quasi-uniform spaces as well as the relationship between (2,M)-fuzzy quasi-uniform spaces and pointwise (L,M)-fuzzy quasi-uniform spaces—the extension of Shi's L-quasi-uniform space in a Kubiak–Šostak sense. It is shown that the category of (2,M)-fuzzy quasi-uniform spaces can be embedded in the category of stratified (L,M)-fuzzy quasi-uniform spaces as a both reflective and coreflective full subcategory; and the former category can also be embedded in the category of pointwise (L,M)-fuzzy quasi-uniform spaces.
Journal: Fuzzy Sets and Systems - Volume 158, Issue 13, 1 July 2007, Pages 1472-1485