Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression Model
A fuzzy set extension known as the hesitant fuzzy set (HFS) has increased in popularity for decision making in recent years, especially when experts have had trouble evaluating several alternatives by employing a single value for assessment when working in a fuzzy environment. However, it has a sign...
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MDPI AG
2022-07-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/22/15/5736 |
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| author | Ayesha Sultan Wojciech Sałabun Shahzad Faizi Muhammad Ismail Andrii Shekhovtsov |
| author_facet | Ayesha Sultan Wojciech Sałabun Shahzad Faizi Muhammad Ismail Andrii Shekhovtsov |
| author_sort | Ayesha Sultan |
| collection | DOAJ |
| description | A fuzzy set extension known as the hesitant fuzzy set (HFS) has increased in popularity for decision making in recent years, especially when experts have had trouble evaluating several alternatives by employing a single value for assessment when working in a fuzzy environment. However, it has a significant problem in its uses, i.e., considerable data loss. The probabilistic hesitant fuzzy set (PHFS) has been proposed to improve the HFS. It provides probability values to the HFS and has the ability to retain more information than the HFS. Previously, fuzzy regression models such as the fuzzy linear regression model (FLRM) and hesitant fuzzy linear regression model were used for decision making; however, these models do not provide information about the distribution. To address this issue, we proposed a probabilistic hesitant fuzzy linear regression model (PHFLRM) that incorporates distribution information to account for multi-criteria decision-making (MCDM) problems. The PHFLRM observes the input–output (IPOP) variables as probabilistic hesitant fuzzy elements (PHFEs) and uses a linear programming model (LPM) to estimate the parameters. A case study is used to illustrate the proposed methodology. Additionally, an MCDM technique called the technique for order preference by similarity to ideal solution (TOPSIS) is employed to compare the PHFLRM findings with those obtained using TOPSIS. Lastly, Spearman’s rank correlation test assesses the statistical significance of two rankings sets. |
| first_indexed | 2024-03-09T05:00:20Z |
| format | Article |
| id | doaj.art-a18de7d843c04ce0afc38088fc882037 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-09T05:00:20Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-a18de7d843c04ce0afc38088fc8820372023-12-03T13:01:25ZengMDPI AGSensors1424-82202022-07-012215573610.3390/s22155736Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression ModelAyesha Sultan0Wojciech Sałabun1Shahzad Faizi2Muhammad Ismail3Andrii Shekhovtsov4Department of Statistics, Lahore Campus, COMSATS University Islamabad, Islamabad 45550, PakistanResearch Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Zołnierska 49, 71-210 Szczecin, PolandDepartment of Mathematics, Virtual University of Pakistan, Lahore 54000, PakistanDepartment of Statistics, Lahore Campus, COMSATS University Islamabad, Islamabad 45550, PakistanResearch Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Zołnierska 49, 71-210 Szczecin, PolandA fuzzy set extension known as the hesitant fuzzy set (HFS) has increased in popularity for decision making in recent years, especially when experts have had trouble evaluating several alternatives by employing a single value for assessment when working in a fuzzy environment. However, it has a significant problem in its uses, i.e., considerable data loss. The probabilistic hesitant fuzzy set (PHFS) has been proposed to improve the HFS. It provides probability values to the HFS and has the ability to retain more information than the HFS. Previously, fuzzy regression models such as the fuzzy linear regression model (FLRM) and hesitant fuzzy linear regression model were used for decision making; however, these models do not provide information about the distribution. To address this issue, we proposed a probabilistic hesitant fuzzy linear regression model (PHFLRM) that incorporates distribution information to account for multi-criteria decision-making (MCDM) problems. The PHFLRM observes the input–output (IPOP) variables as probabilistic hesitant fuzzy elements (PHFEs) and uses a linear programming model (LPM) to estimate the parameters. A case study is used to illustrate the proposed methodology. Additionally, an MCDM technique called the technique for order preference by similarity to ideal solution (TOPSIS) is employed to compare the PHFLRM findings with those obtained using TOPSIS. Lastly, Spearman’s rank correlation test assesses the statistical significance of two rankings sets.https://www.mdpi.com/1424-8220/22/15/5736PHFSFLRMPHFLRMpeters modelMCDM |
| spellingShingle | Ayesha Sultan Wojciech Sałabun Shahzad Faizi Muhammad Ismail Andrii Shekhovtsov Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression Model Sensors PHFS FLRM PHFLRM peters model MCDM |
| title | Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression Model |
| title_full | Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression Model |
| title_fullStr | Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression Model |
| title_full_unstemmed | Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression Model |
| title_short | Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression Model |
| title_sort | making group decisions within the framework of a probabilistic hesitant fuzzy linear regression model |
| topic | PHFS FLRM PHFLRM peters model MCDM |
| url | https://www.mdpi.com/1424-8220/22/15/5736 |
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