In this paper, with the aid of fuzzy soft \(\beta \)-neighborhoods, we introduce fuzzy soft covering-based multi-granulation fuzzy rough set models. We examine some of the relevant properties of fuzzy soft covering based on optimistic, pessimistic, and variable precision multi-granulation fuzzy rough set models. Then, we give fuzzy soft coverings based on \(\psi \)-optimistic and \({\mathscr {D}}\)-optimistic (\(\psi \)-pessimistic and \({\mathscr {D}}\)-pessimistic) multi-granulation fuzzy rough sets from fuzzy soft measures. It also discusses the interactions between these forms of fuzzy soft coverings based on multi-granulation fuzzy rough sets. Eventually, we apply the proposed models for solving MAGDM problems. The effectiveness and feasibility of our approach are noted from the introduced comparisons between our method and some methods given in the previous studies.

本文借助模糊软\（\ beta \）邻域，介绍了基于模糊软覆盖的多粒度模糊粗糙集模型。我们基于乐观，悲观和可变精度多粒度模糊粗糙集模型，研究了模糊软覆盖的一些相关属性。然后，我们基于\（\ psi \）- optimistic和\（{\ mathscr {D}} \）- optimistic（\（\ psi \） -悲观和\（{\ mathscr {D}} \）-悲观的）多粒度模糊粗糙集从模糊软测度。它还讨论了基于多粒度模糊粗糙集的这些形式的模糊软覆盖之间的相互作用。最终，我们将提出的模型用于解决MAGDM问题。从我们的方法与先前研究中给出的一些方法之间的比较中可以注意到我们方法的有效性和可行性。