As a generalization of Zhan’s method (i.e., to increase the lower approximation and decrease the upper approximation), the present paper aims to define the family of complementary fuzzy -neighborhoods and thus three kinds of covering-based multigranulation ()-fuzzy rough sets models are established. Their axiomatic properties are investigated. Also, six kinds of covering-based variable precision multigranulation ()-fuzzy rough sets are defined and some of their properties are studied. Furthermore, the relationships among our given types are discussed. Finally, a decision-making algorithm is presented based on the proposed operations and illustrates with a numerical example to describe its performance.

中文翻译：

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某些类型的基于覆盖的多粒度（）-模糊粗糙集及其在决策中的应用

如詹氏法的一般化（即，为了增加下近似和降低上近似），本文件的目的，以限定互补模糊的家庭-街区和由此3种覆盖基multigranulation的（）-建立了模糊粗糙集模型。研究了它们的公理特性。此外，还有六种基于覆盖的可变精度多重制粒（）-定义了模糊粗糙集并研究了它们的一些特性。此外，讨论了我们给定类型之间的关系。最后，基于所提出的操作，提出了一种决策算法，并通过一个数值示例说明了该算法的性能。