Abstract Aiming at expanding the application range of the multigranulation rough set (MGRS) theory, a type-2 fuzzy multigranulation rough set (T2FMGRS) model is proposed by combining type-2 fuzzy sets with multigranulation rough sets (MGRSs) in this paper. At first, definitions and properties of optimistic and pessimistic type-2 fuzzy multigranulation rough sets (T2FMGRSs) are introduced. Then, the rough measure is proposed to measure the uncertainty of T2FMGRSs. Finally, T2FMGRSs over two universes are put forward and some examples of decision-making are given to illustrate the applicability of the newly proposed model. In summary, the establishment of T2FMGRSs is a meaningful generalization of the MGRS theory from both theoretical and practical aspects.

中文翻译：

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Type-2 模糊多粒度粗糙集

摘要 为了扩大多粒度粗糙集(MGRS)理论的应用范围，本文将2类模糊集与多粒度粗糙集(MGRSs)相结合，提出了2类模糊多粒度粗糙集(T2FMGRS)模型。首先，介绍了乐观和悲观二类模糊多粒度粗糙集（T2FMGRS）的定义和性质。然后，提出了粗略的措施来衡量T2FMGRSs的不确定性。最后，提出了两个宇宙的T2FMGRSs，并给出了一些决策的例子来说明新提出的模型的适用性。综上所述，T2FMGRSs 的建立是对 MGRS 理论从理论和实践两个方面的有意义的概括。