Intuitionistic fuzzy multigranulation rough sets

Exploring rough sets from the perspective of multigranulation represents a promising direction in rough set theory, where concepts are approximated by multiple granular structures represented by binary relations. Through a combination of multigranulation rough sets with intuitionistic fuzzy rough sets, this study develops a new multigranulation rough set model, called an intuitionistic fuzzy multigranulation rough set (IFMGRS). In the multigranulation framework, three types of IFMGRSs that are generalizations of three existing intuitionistic fuzzy rough set models are proposed. First, we present three types of IFMGRSs. From their basic properties, we conclude that they are extensions of three existing intuitionistic fuzzy rough sets. Second, we define the reducts of the three types of IFMGRSs to eliminate redundant intuitionistic fuzzy granulations. Third, we examine the reduction approaches of IFMGRS with a detailed example and discuss the general reduction theory of IFMGRS.