The theory of global fuzzy neighborhood structures (II). Fuzzy topogenous orders

This paper deals with fuzzy topogenous orders, in particular, with fuzzy topogenous structures and with the more special fuzzy proximities. These structures have been investigated ay Katsaras and Petalas (1983, 1984). The notion of fuzzy proximity was introduced by Katsaeas (1980). Fuzzy topogenous...

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Bibliographic Details
Published in:Fuzzy sets and systems 1998-09, Vol.98 (2), p.153-173
Main Authors: Gähler, Werner, Bayoumi, Fatma, Kandil, Ali, Nouh, Ali
Format: Article
Language:English
Subjects:
Fuzzy filters
Fuzzy pretopologies
Fuzzy proximities
Fuzzy topogenous orders and fuzzy topogenous structures
Fuzzy topologies
Global fuzzy neighborhood prestructures
Global fuzzy neighborhood structures
Monadic topologies
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Summary:This paper deals with fuzzy topogenous orders, in particular, with fuzzy topogenous structures and with the more special fuzzy proximities. These structures have been investigated ay Katsaras and Petalas (1983, 1984). The notion of fuzzy proximity was introduced by Katsaeas (1980). Fuzzy topogenous structures and fuzzy proximities are represented in this paper as global fuzzy neighborhood structures. Fuzzy topogenous orders, in general, are characterized by the notion of global fuzzy neighborhood prestructure, which is a weakening of that one of global fuzzy neighborhood structure. In this paper, moreover, a modification of the notion of fuzzy proximity is considered, called fuzzy proximity of the internal type. Whereas the notion of fuzzy proximity proposed by Katsaras depends on a fixed order-reversing involution of the related lattice L, the notion of fuzzy proximity of the internal type is independent on such an involution. The investigations intthis paper demonstrate that there are important global fuzzy neighborhood structures and prestructures different from fuzzy topologies and fuzzy pretopologies, respectively.
ISSN:0165-0114
1872-6801
DOI:10.1016/S0165-0114(97)00346-1