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

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 pro...

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Bibliographic Details
Published in:IEEE access 2022, Vol.10, p.46936-46962
Main Authors: Gul, Rizwan, Shabir, Muhammad, Aslam, Muhammad, Naz, Shafaq
Format: Article
Language:English
Subjects:
Approximation
Astronomical models
Biological system modeling
Comparative studies
Decision making
Decision theory
Diseases
Granulation
Mathematical analysis
Mathematical models
MCGDM
Measurement uncertainty
Medical diagnosis
MGMRBS-approximations
MGRS
MRBSs
Multiple criterion
Problem solving
Rough sets
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Summary: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 decision-making (MCGDM) approach based on OMGMRBSs is developed to solve some problems in decision-making (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.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2022.3169738