Multigranulation Modified Rough Bipolar Soft Sets and Their Applications in Decision-Making

Abstract

The classical theory of rough sets (RSs) established by Pawlak, mainly focused on the approximation of sets characterized by a single equivalence relation (ER) over the universe. However, most of the current single granulation structure models cannot meet the user demand or the target of solving problems. Multi-granulation rough sets (MGRS) can better deal with the problems where data might be spread over various locations. In this article, based on modified rough bipolar soft sets (MRBSs), the concept of multi-granulation MRBSs (MGMRBSs) is introduced. A finite collection of bipolar soft sets (BSs) has been used for this purpose. Several important structural properties and results of the suggested model are carefully analyzed. Meanwhile, to measure the uncertainty of MGMRBSs, some important measures associated with MGMRBSs are presented in MGMRBS-approximation space, and some of their interesting properties are examined. In the framework of multi-granulation, we developed optimistic MGMRBSs (OMGMRBSs) and pessimistic MGMRBSs (PMGMRBSs). The relationships among the MGMRBSs, OMGMRBSs, and PMGMRBSs are also established. After that, a novel multi-criteria group decisionmaking (MCGDM) approach based on OMGMRBSs is developed to solve some problems in decisionmaking (DM). The basic principles and the detailed steps of the DM model are presented in detail. To demonstrate the applicability and potentiality of the developed model, we give a practical example of a medical diagnosis. Finally, we conduct a comparative study of the proposed MCGDM approach with some existing techniques to endorse the advantages of the proposed model.INDEX TERMS MGRS, MRBSs, MGMRBS-approximations, MCGDM.

A novel multigranulation roughness of bipolar fuzzy set over dual universes and its applications

“…(iii) If we implement the presently available decision-making approaches described in [33,34], and [36] to our Example 6.1, we get the following ranking among the diseases (shown in table 16 ), we find that the best and worst solutions through all methods is identical, showing the viability and efficiency of our method.…”

“…(i) In this research, we define the optimistic multigranulation roughness of BFS over dual universes in light of soft binary relations. The other methods described in [30,34,36] are based on general binary relations. These methods define the multigranulation roughness of a given set using general binary relations.…”

“…(ii) The multigranulation roughness of BFS defines the degree of accuracy measure and roughness measure, on the other hand, the methods described in [13,25,30,33,34], and [36] are unable to define these measures. These measures investigate how accurately the membership maps of OMGRBFS describe the objects.…”

“…Anwer et al [33] proposed multi soft Brs-based MGRS scheme of intuitionistic FS and their applications in DM issues. Gul et al [34] presented multi BSS-based MGRS of modified rough BSSs and their applications in DM issues.…”

Linear Diophantine Fuzzy Aggregation Operators with Multi-Criteria Decision-Making

“…Riaz et al proposed a number of AOs, including interactive Riaz, Garg, et al (2021) and prioritized with PDs . Some extra-ordinary work related to proposed work is given in Karaaslan and Ozlu (2020); Din et al (2022); Gul et al (2022); Alcantud (2022). Akram et al (2021) gave the idea of Pythagorean ELECTRE-II approach.…”