Inclusion measure-based multi-granulation intuitionistic fuzzy decision-theoretic rough sets and their application to ISSA

Decision-theoretic rough set (DTRS) and multi-granulation rough set (MGRS) are two important extended types of Pawlak's classical rough set model. The two generalized rough sets have been investigated separately by numerous researchers. However, few studies have focused on the combination of the two rough sets in intuitionistic fuzzy (IF) settings. In this study, two novel MG-IF-DTRS models, which are generalizations of MG-DTRSs, are developed by exploring DTRS and MGRS based on IF inclusion measures to explore multi-granulation IF DTRS (MG-IF-DTRS) under IF information environment. We introduce a type of inclusion measure between two IF sets and present the concept of inclusion measure-based IF-DTRS. We verify whether the model is an extension of the classical DTRS. Second, we present the inclusion measure-based optimistic and pessimistic MG-IF-DTRSs, analyze their properties, and conclude that the presented MG-IF-DTRSs are generalizations of MG-DTRSs from the viewpoint of multi-granulation. We then study the discernibility-function-based reduction methods for the presented MG-IF-DTRSs. We also provide an illustrative example of information system security audit to verify the established approach and demonstrate its validity and applicability. Finally, we discuss several possible generalizations related to MG-IF-DTRSs. This study provides a MG-IF-DTRS method for acquiring knowledge from multi-granulation IF decision systems.