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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9762900/ |
| _version_ | 1811338696110112768 |
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| author | Rizwan Gul Muhammad Shabir Muhammad Aslam Shafaq Naz |
| author_facet | Rizwan Gul Muhammad Shabir Muhammad Aslam Shafaq Naz |
| author_sort | Rizwan Gul |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T18:14:57Z |
| format | Article |
| id | doaj.art-3db58fe9830a4613a62a2e16e03e155b |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-13T18:14:57Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-3db58fe9830a4613a62a2e16e03e155b2022-12-22T02:35:43ZengIEEEIEEE Access2169-35362022-01-0110469364696210.1109/ACCESS.2022.31697389762900Multigranulation Modified Rough Bipolar Soft Sets and Their Applications in Decision-MakingRizwan Gul0https://orcid.org/0000-0002-6139-1872Muhammad Shabir1Muhammad Aslam2Shafaq Naz3Department of Mathematics, Quaid-i-Azam University, Islamabad, PakistanDepartment of Mathematics, Quaid-i-Azam University, Islamabad, PakistanDepartment of Mathematics, College of Sciences, King Khalid University, Abha, Saudi ArabiaDepartment of Mathematics, University of Gujrat, Gujrat, PakistanThe 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.https://ieeexplore.ieee.org/document/9762900/MGRSMRBSsMGMRBS-approximationsMCGDM |
| spellingShingle | Rizwan Gul Muhammad Shabir Muhammad Aslam Shafaq Naz Multigranulation Modified Rough Bipolar Soft Sets and Their Applications in Decision-Making IEEE Access MGRS MRBSs MGMRBS-approximations MCGDM |
| title | Multigranulation Modified Rough Bipolar Soft Sets and Their Applications in Decision-Making |
| title_full | Multigranulation Modified Rough Bipolar Soft Sets and Their Applications in Decision-Making |
| title_fullStr | Multigranulation Modified Rough Bipolar Soft Sets and Their Applications in Decision-Making |
| title_full_unstemmed | Multigranulation Modified Rough Bipolar Soft Sets and Their Applications in Decision-Making |
| title_short | Multigranulation Modified Rough Bipolar Soft Sets and Their Applications in Decision-Making |
| title_sort | multigranulation modified rough bipolar soft sets and their applications in decision making |
| topic | MGRS MRBSs MGMRBS-approximations MCGDM |
| url | https://ieeexplore.ieee.org/document/9762900/ |
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