An Extension Principle for Closure Operators
An Extension Principle for Closure Operators
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DOI：
10.1006/jmaa.1996.0064
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发表时间：
1996-02
影响因子：
1.3
通讯作者：
L. Biacino;Giangiacomo Gerla
中科院分区：
文献类型：
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作者：
L. Biacino;Giangiacomo Gerla
这导致一些作者在模糊集理论的框架内研究闭包系统和闭包算子。由此产生的研究对模糊 Ž w x 子代数、必要性测度和包络等概念进行了优雅而有力的处理，例如，参见 1]4 和 w x。 11. Ž 。 Ž 。令S为任意集合，并用P S 和F S 分别表示S的子集类和模糊子集类。在本文中，我们提出了一个“扩展原则”，使我们能够扩展任何经典的 Ž 。 Ž 。 Ž 。 Ž 。运算符 J: P S a P S 到运算符 J*: F S a F S 的方式是，当且仅当 J 是闭包运算符时，J* 才是闭包运算符。另外，我们
This led several authors to investigate the closure systems and the closure operators in the framework of fuzzy set theory. The resulting researches give an elegant and powerful treatment of notions such as those of fuzzy Ž w x subalgebras, necessity measures, and envelopes for example, see 1]4 and w x. 11 . Ž . Ž . Let S be any set, and denote by P S and F S the class of the subsets and the class of the fuzzy subsets of S, respectively. In this paper we propose an ‘‘extension principle’’ enabling us to extend any classical Ž . Ž . Ž . Ž . operator J: P S a P S to an operator J*: F S a F S in such a way that J* is a closure operator if and only if J is a closure operator. Also, we