Recently, the concept of a soft rough fuzzy covering (briefly, SRFC) by means of soft neighborhoods was defined and their properties were studied by Zhan’s model. As a generalization of Zhan’s method and in order to increase the lower approximation and decrease the upper approximation, the present work aims to define the complementary soft neighborhood and hence three types of soft rough fuzzy covering models (briefly, 1-SRFC, 2-SRFC, and 3-SRFC) are proposed. We discuss their axiomatic properties. According to these results, we investigate three types of fuzzy soft measure degrees (briefly, 1-SMD, 2-SMD, and 3-SMD). Also, three kinds of -soft rough fuzzy coverings (briefly, 1--SRFC, 2--SRFC, and 3--SRFC) and three kinds of -soft rough fuzzy coverings (briefly, 1--SRFC, 2--SRFC, and 3--SRFC) are discussed and some of their properties are studied. Finally, the relationships among these three models and Zhan’s model are presented.

中文翻译：

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基于软粗糙覆盖的三种模糊集

最近，定义了通过软邻域进行软粗糙模糊覆盖（简称SRFC）的概念，并通过詹的模型研究了它们的性质。作为詹方法的推广，为了增加下近似值并减小上近似值，本工作旨在定义互补的软邻域，因此定义了三种类型的软粗糙模糊覆盖模型（简而言之，1-SRFC，2-SRFC ，和3-SRFC）。我们讨论它们的公理特性。根据这些结果，我们研究了三种类型的模糊软测量度（简称为1-SMD，2-SMD和3-SMD）。另外，3种-软粗模糊覆盖物（简要地，1- - SRFC，2- - SRFC，和3- - SRFC）和3种-软粗模糊覆盖物（简要地，1- - SRFC，2- - SRFC，和3- - SRFC）进行了讨论和它们的一些性质进行了研究。最后，介绍了这三个模型与詹氏模型之间的关系。