Multi-granulation Pythagorean fuzzy decision-theoretic rough sets based on inclusion measure and their application in incomplete multi-source information systems

Abstract

Multi-granulation rough sets (MGRSs) and decision-theoretic rough sets (DTRSs) are two important and popular generalizations of classical rough sets. The combination of two generalized rough sets have been investigated by numerous researchers in different extensions of fuzzy settings such as interval-valued fuzzy sets (IVFSs), intuitionistic fuzzy sets (IFSs), bipolar-valued fuzzy sets (BVFSs), etc. Pythagorean fuzzy (PF) set is another extension of fuzzy set, which is more capable in comparison to IFS handle vagueness in real world. However, few studies have focused on the combination of the two rough sets in PF settings. In this study, we combine the two generalized rough sets in PF settings. First, we introduce a type of PF subset (of subset of the given universe) of the PF Set (of the given universe). Then we establish two basic models of multi-granulation PF DTRS (MG-PF-DTRS) of PF subset of the PF set based on PF inclusion measure within the framework of multi-granulation PF approximation space. One model is based on a combination of PF relations (PFRs) and the construction of approximations with respect to the combined PFR. By combining PFRs through intersection and union, respectively, we construct two models. The other model is based on the construction of approximations from PFRs and a combination of the approximations. By using intersection and union to combine the approximations, respectively, we again get two models. As a result, we have total four models. Further for different constraints on parameters, we obtain three kinds of each model of the MG-PF-DTRSs. Then, their principal structure, basic properties and uncertainty measure methods are investigated as well. Second, we give a way to compute PF similarity degrees between two objects and also give a way to compute PF decision-making objects from incomplete multi-source information systems (IMSISs). Then we design an algorithm for decision-making to IMSISs using MG-PFDTRSs and their uncertainty measure methods. Finally, an example about the mutual funds investment is included to show the feasibility and potential of the theoretic results obtained.

KNNHI: Resilient KNN algorithm for heterogeneous incomplete data classification and K identification using rough set theory

“…Others tackle the incompleteness problem by eliminating the objects with missing values, especially if the proportion of those objects is not high, as in Alloghani et al [26], where the authors excluded 21 objects containing missing values out of 541 objects in the original dataset. In Mandal and Ranadive [27], the incompleteness problem is addressed by a mix of RST and fuzzy set notions.…”

Conflict distance-based variable precision Pythagorean fuzzy rough set in Pythagorean fuzzy decision systems with applications in decision making

“…They used Pythagorean fuzzy numbers (PFNs) to obtain loss functions and proposed group decision-making (GDM) based on Pythagorean fuzzy DTRS (PFDTRS). In [11], Mandal and Ranadive propose a new method for dealing with multi-criteria decision-making (MCDM) problems that involve Pythagorean fuzzy information (PFI) with different levels of granularity. The method combines two extensions of classical rough sets: multi-granulation rough sets (MGRSs) and DTRSs.…”

Optimistic multigranulation roughness of fuzzy bipolar soft sets by soft binary relations and its applications

“…Chan and Xu [30] proposed the multigranulation rough fuzzy set based on logical operations and application in MCGDM. Mandal and Ranadive [31] put forth the multigranulation roughness of decision-theoretic rough sets and its application in an incomplete information system. Mubarak et al [32] presented the optimistic multigranulation roughness of bipolar fuzzy set over dual universes.…”