基于模糊覆盖的广义模糊粗糙集
Generalized fuzzy rough sets based on fuzzy coverings
摘要：
本文进一步研究了基于模糊覆盖的模糊粗糙集。我们首先提出了基于模糊覆盖的上、下近似算子的概念，并推导了它们的基本性质。为了方便模糊覆盖粗糙集的模糊覆盖计算，给出了模糊子覆盖、可约元、交元、并运算、交运算等概念，并详细讨论了它们的性质.随后，我们引入了一致函数和模糊覆盖映射的概念，为模糊覆盖信息系统之间的通信提供了基本的理论基础。此外，还提出了同态的概念来揭示模糊覆盖信息系统之间的关系。我们展示了如何大规模的模糊覆盖信息系统和动态模糊覆盖信息系统可以转化为小规模的同态。最后，一个说明性的例子表明，我们提出的方法可以大大简化属性约简。
英文摘要：
This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation of fuzzy coverings for fuzzy covering rough sets, the concepts of fuzzy subcoverings, the reducible and intersectional elements, the union and intersection operations are provided and their properties are discussed in detail. Afterwards, we introduce the concepts of consistent functions and fuzzy covering mappings and provide a basic theoretical foundation for the communication between fuzzy covering information systems. In addition, the notion of homomorphisms is proposed to reveal the relationship between fuzzy covering information systems. We show how large-scale fuzzy covering information systems and dynamic fuzzy covering information systems can be converted into small-scale ones by means of homomorphisms. Finally, an illustrative example is employed to show that the attribute reduction can be simplified significantly by our proposed approach.
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