THE THEORY OF GLOBAL FUZZY NEIGHBORHOOD STRUCTURES - (II) - FUZZY TOPOGENOUS ORDERS

Citation
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
Journal title
ISSN journal
01650114
Volume
98
Issue
2
Year of publication
1998
Pages
153 - 173
Database
ISI
SICI code
0165-0114(1998)98:2<153:TTOGFN>2.0.ZU;2-E
Abstract
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.