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Topological interpretations of fuzzy subsets. A unified approach for fuzzy thresholding algorithms

机译：模糊子集的拓扑解释。模糊阈值算法的统一方法

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摘要

We show that the classical definition of a fuzzy subset carries additional structures of a topological nature. We look at the concept of a fuzzy subset and its corresponding α-cuts from an alternative point of view: namely, a fuzzy subset may be interpreted as a nested topology on a crisp set of reference, called a universe. Several kinds of fuzzy subsets associated to this interpretation are analyzed. Other topologies induced by fuzzy subsets are considered, paying special attention to their relationship with total preorders defined on the universe. Moreover, this theoretical approach allows us to provide a unified framework for most of the fuzzy thresholding algorithms that can be found in the literature.
机译：我们表明模糊子集的经典定义带有拓扑性质的其他结构。我们从另一个角度来看模糊子集及其对应的α割的概念：即，模糊子集可以解释为在称为Universe的一组清晰参考上的嵌套拓扑。分析了与此解释相关的几种模糊子集。考虑了由模糊子集引起的其他拓扑，要特别注意它们与宇宙中定义的总预序的关系。此外，这种理论方法使我们能够为文献中可以找到的大多数模糊阈值算法提供一个统一的框架。

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