THE THEORY OF GLOBAL FUZZY NEIGHBORHOOD STRUCTURES - (III) - FUZZY UNIFORM STRUCTURES

In this paper a new notion of fuzzy uniform structure is presented and investigated. Fuzzy uniform structures are given as special fuzzy fil ters. Of special interest are those fuzzy uniform structures which are sup-fuzzy filters. They can be characterized by a related notion of f uzzy syntopogenous structure. As is shown, fuzzy metrics (Gahler and G ahler, 1994) generate fuzzy uniform structures in our sense. Each fuzz y uniform structure has an associated global homogeneous fuzzy neighbo rhood structure and hence also an associated fuzzy topology. In case o f a 0, 1-fuzzy uniform structure and even in a more general case, a fu zzy uniform structure of the first type can be associated There are gi ven relation to Huttons's and Katsaras' notions of fuzzy uniform struc ture (Hutton, 1977; Katsaras, 1979) and to the notion of fuzzy syntopo genous structure in sense of Katsaras and Petalas (1984). (C) 1998 Els evier Science B.V. All rights reserved.