The Fuzzy Sets with Continuous Membership Functions in Topological Spaces

拓樸空間具備連續歸屬函數的模糊集

黃敏昌(Min-Chan Hwang)

《先進工程學刊》 4卷2期 (2009/04) Pp. 147-150

https://doi.org/10.29948/JAE.200904.0008

摘要

本文目的是將模糊集概念從實數空間推廣至拓樸空間。如果明確集是巢狀結構且其集合的包含順序與其索引在實軸上的秩序呈逆向關係，那麼這些明確集可構成模糊集。再者，如果在正規空間裏從開集建造起模糊集，則永遠可以賦予模糊集一連續的歸屬函數。

關鍵字

模糊集 ； 拓樸空間 ； 連續

並列摘要

The objective of this paper is to generalize the concept of fuzzy sets from a real space to a topological space. If the crisp sets are nested and ordered by set inclusion in the reverse way that their subscripts are ordered by the usual ordering in the real line, they can constitute a fuzzy set. Moreover, it is always feasible to construct a fuzzy set which possesses a continuous membership function on a normal space if the crisp set from which a fuzzy set is constructed is a nonempty open set.

並列關鍵字

fuzzy set ； topological space ； continuous