Three-way decision models based on multigranulation support intuitionistic fuzzy rough sets

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.