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期刊名称: Fuzzy Sets and Systems
Volume:31    Issue:1        Page:83-109
ISSN:0165-0114

Nearness concepts in fuzzy neighbourhood spaces and in their fuzzy proximity spaces期刊论文

作者: Morsi Nehad N
DOI:10.1016/0165-0114(89)90069-9

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页码: 83-109
被引频次: 30
出版者: Elsevier B.V,ELSEVIER SCIENCE BV
期刊名称: Fuzzy Sets and Systems
ISSN: 0165-0114
卷期: Volume:31    Issue:1
语言: English
摘要: The nearness concept giving rise to a fuzzy topological space is a fuzzy relation of closeness between fuzzy subsets and crisp points of the space. Lowen [8] introduced the category of fuzzy neighbourhood spaces, which we denote by FNS. His heuristic idea was that the fuzzy topologies in FNS should be characterized by means of fuzzy neighbourhoods of crisp points. It may be argued that the 'fuzziness' of some concepts related to FNS is rather restricted. But, besides the benefits gained from this restriction in that FNS is a category of 'well behaved' fuzzy topological spaces (cf. [1, 5, 8, 9, 14, 17, 18]), we argue in this paper that this restriction acts to reduce the above mentioned concept of nearness to the following one:. The nearness concept giving rise to a fuzzy neighbourhood space is a fuzzy relation of closeness between the crisp subsets and the crisp points of the space. Such fuzzy relation may naturally arise when fuzziness is engrained in the definition of the points of the space; for instance in the fuzzy unit interval of Hutton [4]. Artico and Moresco [2] introduced a concept of fuzzy proximities. We show that this concept is particular to fuzzy neighbourhood spaces only. We then argue that the nearness concept giving rise to a fuzzy proximity space is a fuzzy relation of proximity defined on all pairs of crisp subsets of the space. © 1989.
相关主题: fuzzy proximal neighbourhood system, Fuzzy neighbourhood space, measurable system of topologies, fuzzy uniform space, fuzzy proximity space, MATHEMATICS, APPLIED, STATISTICS & PROBABILITY, COMPUTER SCIENCE, THEORY & METHODS,

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