W. Gahler et al., THE THEORY OF GLOBAL FUZZY NEIGHBORHOOD STRUCTURES - (II) - FUZZY TOPOGENOUS ORDERS, Fuzzy sets and systems, 98(2), 1998, pp. 153-173
Citations number
26
Categorie Soggetti
Statistic & Probability",Mathematics,"Computer Science Theory & Methods","Statistic & Probability",Mathematics,"Computer Science Theory & Methods
This paper deals with fuzzy topogenous orders, in particular, with fuz
zy topogenous structures and with the more special fuzzy proximities.
These structures have been investigated by Katsaras and Petalas (1983,
1984). The notion of fuzzy proximity was introduced by Katsaras (1980
). Fuzzy topogenous structures and fuzzy proximities are represented i
n this paper as global fuzzy neighborhood structures. Fuzzy topogenous
orders, in general, are characterized by the notion of global fuzzy n
eighborhood prestructure, which is a weakening of that one of global f
uzzy neighborhood structure. In this paper, moreover, a modification o
f the notion of fuzzy proximity is considered, called fuzzy proximity
of the internal type. Whereas the notion of fuzzy proximity proposed b
y Katsaras depends on a fixed order-reversing involution of the relate
d lattice L, the notion of fuzzy proximity of the internal type is ind
ependent on such an involution. The investigations in this paper demon
strate that there are important global fuzzy neighborhood structures a
nd prestructures different from fuzzy topologies and fuzzy pretopologi
es, respectively. (C) 1998 Elsevier Science B.V. All rights reserved.