A Comprehensive study on (α,β)-multi-granulation bipolar fuzzy rough sets under bipolar fuzzy preference relation
The rough set (RS) and multi-granulation RS (MGRS) theories have been successfully extended to accommodate preference analysis by substituting the equivalence relation (ER) with the dominance relation (DR). On the other hand, the bipolar fuzzy sets (BFSs) are effective tools for handling bipolarity...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231320?viewType=HTML |
| _version_ | 1797674333754097664 |
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| author | Rizwan Gul Muhammad Shabir Tareq M. Al-shami M. Hosny |
| author_facet | Rizwan Gul Muhammad Shabir Tareq M. Al-shami M. Hosny |
| author_sort | Rizwan Gul |
| collection | DOAJ |
| description | The rough set (RS) and multi-granulation RS (MGRS) theories have been successfully extended to accommodate preference analysis by substituting the equivalence relation (ER) with the dominance relation (DR). On the other hand, the bipolar fuzzy sets (BFSs) are effective tools for handling bipolarity and fuzziness of the data. In this study, with the description of the background of risk decision-making problems in reality, we present $ (\alpha, \beta) $-optimistic multi-granulation bipolar fuzzified preference rough sets ($ (\alpha, \beta)^o $-MG-BFPRSs) and $ (\alpha, \beta) $-pessimistic multi-granulation bipolar fuzzified preference rough sets ($ (\alpha, \beta)^p $-MG-BFPRSs) using bipolar fuzzy preference relation (BFPR). Subsequently, the relevant properties and results of both $ (\alpha, \beta)^o $-MG-BFPRSs and $ (\alpha, \beta)^p $-MG-BFPRSs are investigated in detail. At the same time, a relationship among the $ (\alpha, \beta) $-BFPRSs, $ (\alpha, \beta)^o $-MG-BFPRSs and $ (\alpha, \beta)^p $-MG-BFPRSs is given. |
| first_indexed | 2024-03-11T21:57:34Z |
| format | Article |
| id | doaj.art-5331af4114e74b8ab9fc0ae230520f32 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T21:57:34Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-5331af4114e74b8ab9fc0ae230520f322023-09-26T01:35:21ZengAIMS PressAIMS Mathematics2473-69882023-09-01811258882592110.3934/math.20231320A Comprehensive study on (α,β)-multi-granulation bipolar fuzzy rough sets under bipolar fuzzy preference relationRizwan Gul 0 Muhammad Shabir1Tareq M. Al-shami2M. Hosny31. Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan1. Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan2. Department of Mathematics, Sana'a University, Sana'a, Yemen3. Department of Mathematics, Faculty of Science for Girls, King Khalid University, Abha, Saudi ArabiaThe rough set (RS) and multi-granulation RS (MGRS) theories have been successfully extended to accommodate preference analysis by substituting the equivalence relation (ER) with the dominance relation (DR). On the other hand, the bipolar fuzzy sets (BFSs) are effective tools for handling bipolarity and fuzziness of the data. In this study, with the description of the background of risk decision-making problems in reality, we present $ (\alpha, \beta) $-optimistic multi-granulation bipolar fuzzified preference rough sets ($ (\alpha, \beta)^o $-MG-BFPRSs) and $ (\alpha, \beta) $-pessimistic multi-granulation bipolar fuzzified preference rough sets ($ (\alpha, \beta)^p $-MG-BFPRSs) using bipolar fuzzy preference relation (BFPR). Subsequently, the relevant properties and results of both $ (\alpha, \beta)^o $-MG-BFPRSs and $ (\alpha, \beta)^p $-MG-BFPRSs are investigated in detail. At the same time, a relationship among the $ (\alpha, \beta) $-BFPRSs, $ (\alpha, \beta)^o $-MG-BFPRSs and $ (\alpha, \beta)^p $-MG-BFPRSs is given.https://www.aimspress.com/article/doi/10.3934/math.20231320?viewType=HTMLrough setbipolar fuzzy preference relation$ (\alpha\beta)^o $-mg-bfprss\beta)^p $-mg-bfprss |
| spellingShingle | Rizwan Gul Muhammad Shabir Tareq M. Al-shami M. Hosny A Comprehensive study on (α,β)-multi-granulation bipolar fuzzy rough sets under bipolar fuzzy preference relation AIMS Mathematics rough set bipolar fuzzy preference relation $ (\alpha \beta)^o $-mg-bfprss \beta)^p $-mg-bfprss |
| title | A Comprehensive study on (α,β)-multi-granulation bipolar fuzzy rough sets under bipolar fuzzy preference relation |
| title_full | A Comprehensive study on (α,β)-multi-granulation bipolar fuzzy rough sets under bipolar fuzzy preference relation |
| title_fullStr | A Comprehensive study on (α,β)-multi-granulation bipolar fuzzy rough sets under bipolar fuzzy preference relation |
| title_full_unstemmed | A Comprehensive study on (α,β)-multi-granulation bipolar fuzzy rough sets under bipolar fuzzy preference relation |
| title_short | A Comprehensive study on (α,β)-multi-granulation bipolar fuzzy rough sets under bipolar fuzzy preference relation |
| title_sort | comprehensive study on α β multi granulation bipolar fuzzy rough sets under bipolar fuzzy preference relation |
| topic | rough set bipolar fuzzy preference relation $ (\alpha \beta)^o $-mg-bfprss \beta)^p $-mg-bfprss |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231320?viewType=HTML |
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