Inclusion measure-based multi-granulation decision-theoretic rough sets in multi-scale intuitionistic fuzzy information tables

Multi-granulation rough sets (MGRSs) and decision-theoretic rough sets (DTRSs) are important and popular extended types of Pawlak's classical rough set model. Multi-granulation DTRSs (MG-DTRSs), which combine these two generalized rough set models, have been investigated in depth in recent years to handle noisy distributed data. However, this combination cannot be used to acquire knowledge from multi-scale information systems, in which an object may take on different values under the same attribute depending on the scale used to measure it. Two novel types of MG-DTRSs in multi-scale intuitionistic fuzzy (IF) information tables have been developed on the basis of IF inclusion measures in this study to solve this problem. First, we introduce a type of inclusion measure between two IF sets and present the concept of inclusion measure-based DTRSs in multi-scale IF information tables. Second, we present the inclusion measure-based optimistic and pessimistic MG-DTRSs in multi-scale IF information tables, examine their properties, and analyze the three-way decision method based on the presented models. Third, we define the optimal scale selection and present the two optimal scale selection algorithms based on MG-DTRSs in multi-scale IF information tables. Fourth, we provide the reducts of the optimal scales based on MG-DTRSs in multi-scale IF information tables, examine the discernibility function reduction method, and devise two algorithms for computing an optimal approximation scale reduct. Finally, we discuss several possible generalizations related to MG-DTRSs in multi-scale IF information tables. This study provides an MG-DTRS method for acquiring knowledge from multi-scale IF information tables. (C) 2018 Elsevier Inc. All rights reserved.