Abstract To capture the influence of various uncertain factors during delayed decision-making, support intuitionistic fuzzy sets (SIFSs) are introduced for three-way decisions (TWDs) to study this topic from the perspective of multigranulation. First, the concepts of support intuitionistic fuzzy rough sets are defined, and their related properties are discussed. Then, we combine support intuitionistic fuzzy rough sets with multigranulation rough sets (MRSs), present optimistic/pessimistic multigranulation support intuitionistic fuzzy rough set models, and discuss their corresponding properties. Second, a parameter α is introduced to constrain the disjunction and conjunction of multiple support intuitionistic fuzzy relations, and variable optimistic and pessimistic multigranulation support intuitionistic fuzzy rough set models are constructed. Third, we define the similarity measure, positive ideal solution, negative ideal solution, and conditional probability based on multigranulation support intuitionistic fuzzy rough sets. Four kinds of TWD models based on four proposed multigranulation support intuitionistic fuzzy rough set models are established. Finally, decision rules can be obtained from a new score function and accuracy function, and the decision rule extraction algorithm based on multigranulation support intuitionistic fuzzy rough sets is designed. Experimental results on a series of examples demonstrate the effectiveness of our proposed TWD models.

中文翻译：

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基于多粒度的三向决策模型支持直觉模糊粗糙集

摘要 为了捕捉延迟决策过程中各种不确定因素的影响，引入支持直觉模糊集（SIFS）用于三路决策（TWD），从多粒度的角度研究该课题。首先，定义了支持直觉模糊粗糙集的概念，并讨论了它们的相关性质。然后，我们将支持直觉模糊粗糙集与多粒度粗糙集（MRS）相结合，提出了乐观/悲观多粒度支持直觉模糊粗糙集模型，并讨论了它们的相应性质。其次，引入参数α来约束多支持直觉模糊关系的析取和合取，构建了变量乐观和悲观多粒度支持直觉模糊粗糙集模型。第三，我们定义了基于多粒度支持直觉模糊粗糙集的相似性测度、正理想解、负理想解和条件概率。基于所提出的四种多粒度支持直觉模糊粗糙集模型，建立了四种TWD模型。最后，从新的评分函数和准确度函数中获取决策规则，设计了基于多粒度支持直觉模糊粗糙集的决策规则提取算法。一系列示例的实验结果证明了我们提出的 TWD 模型的有效性。基于所提出的四种多粒度支持直觉模糊粗糙集模型，建立了四种TWD模型。最后，从新的评分函数和准确度函数中得到决策规则，设计了基于多粒度支持直觉模糊粗糙集的决策规则提取算法。一系列示例的实验结果证明了我们提出的 TWD 模型的有效性。基于所提出的四种多粒度支持直觉模糊粗糙集模型，建立了四种TWD模型。最后，从新的评分函数和准确度函数中得到决策规则，设计了基于多粒度支持直觉模糊粗糙集的决策规则提取算法。一系列示例的实验结果证明了我们提出的 TWD 模型的有效性。