The theory of global fuzzy neighborhood structures. III: Fuzzy uniform structures
This is the third part of a series by the authors, in the first and the second parts they introduced global fuzzy neighbourhood structures and global fuzzy neighbourhood prestructures with respect to the partially ordered fuzzy filter monad. In this part the authors continue their research to establish a theory of fuzzy uniformity by means of fuzzy filters. After some necessary preparation on fuzzy filters on \(X\times X\), they define fuzzy uniformity on a set \(X\) as a special fuzzy filter on \(X\times X\) analogous to A. Weil's definition of uniformity. Relationships to fuzzy syntopogeneous structures, Katsaras fuzzy uniformity, fuzzy topology and global fuzzy neighbourhood structures, etc., are systematically investigated.
scientific article; zbMATH DE number 1320380
scientific article