A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital Assessment
The probabilistic linguistic term set (PLTS) is a newly emerging mathematical tool for handling uncertainties. It is considered a useful extension of linguistic term sets associated with probability information and can improve the effectiveness of multiple attribute decision making (MADM). This pape...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/8/3/340 |
| _version_ | 1819330923909349376 |
|---|---|
| author | Dandan Luo Shouzhen Zeng Ji Chen |
| author_facet | Dandan Luo Shouzhen Zeng Ji Chen |
| author_sort | Dandan Luo |
| collection | DOAJ |
| description | The probabilistic linguistic term set (PLTS) is a newly emerging mathematical tool for handling uncertainties. It is considered a useful extension of linguistic term sets associated with probability information and can improve the effectiveness of multiple attribute decision making (MADM). This paper proposes a new PLTS correlation coefficient and addresses its usefulness in MADM problems. For achieving this aim, some new concepts of mean, variance, and covariance of the PLTS are first proposed. Moreover, a novel PLTS Pearson correlation coefficient is defined to overcome the shortcomings of the existing methods, whose significant feature is that it lies in the interval [−1,1], which makes it more effective in reflecting the negative and positive correlation between PLTSs. A weighted PLTS Pearson correlation coefficient is further defined to consider the importance of attribute weights and expand the scope of application. Then, a relative PLTS closeness coefficient is constructed based on the developed Pearson correlation coefficient, and based on which, a Pearson correlation-based TOPSIS (technique for order of preference by similarity to ideal solution) approach for MADM problems is developed. Finally, the effectiveness as well as the applicability of the developed method are illustrated through numerical examples and comparative analysis. |
| first_indexed | 2024-12-24T14:06:15Z |
| format | Article |
| id | doaj.art-b439b8ec55e44544b7dfee5d4dc953b0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-24T14:06:15Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b439b8ec55e44544b7dfee5d4dc953b02022-12-21T16:52:20ZengMDPI AGMathematics2227-73902020-03-018334010.3390/math8030340math8030340A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital AssessmentDandan Luo0Shouzhen Zeng1Ji Chen2School of Business, Ningbo University, Ningbo 315211, ChinaSchool of Business, Ningbo University, Ningbo 315211, ChinaCollege of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, ChinaThe probabilistic linguistic term set (PLTS) is a newly emerging mathematical tool for handling uncertainties. It is considered a useful extension of linguistic term sets associated with probability information and can improve the effectiveness of multiple attribute decision making (MADM). This paper proposes a new PLTS correlation coefficient and addresses its usefulness in MADM problems. For achieving this aim, some new concepts of mean, variance, and covariance of the PLTS are first proposed. Moreover, a novel PLTS Pearson correlation coefficient is defined to overcome the shortcomings of the existing methods, whose significant feature is that it lies in the interval [−1,1], which makes it more effective in reflecting the negative and positive correlation between PLTSs. A weighted PLTS Pearson correlation coefficient is further defined to consider the importance of attribute weights and expand the scope of application. Then, a relative PLTS closeness coefficient is constructed based on the developed Pearson correlation coefficient, and based on which, a Pearson correlation-based TOPSIS (technique for order of preference by similarity to ideal solution) approach for MADM problems is developed. Finally, the effectiveness as well as the applicability of the developed method are illustrated through numerical examples and comparative analysis.https://www.mdpi.com/2227-7390/8/3/340probabilistic linguistic term settopsispearson correlation coefficientmultiple attribute decision makinghospital assessment |
| spellingShingle | Dandan Luo Shouzhen Zeng Ji Chen A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital Assessment Mathematics probabilistic linguistic term set topsis pearson correlation coefficient multiple attribute decision making hospital assessment |
| title | A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital Assessment |
| title_full | A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital Assessment |
| title_fullStr | A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital Assessment |
| title_full_unstemmed | A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital Assessment |
| title_short | A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital Assessment |
| title_sort | probabilistic linguistic multiple attribute decision making based on a new correlation coefficient method and its application in hospital assessment |
| topic | probabilistic linguistic term set topsis pearson correlation coefficient multiple attribute decision making hospital assessment |
| url | https://www.mdpi.com/2227-7390/8/3/340 |
| work_keys_str_mv | AT dandanluo aprobabilisticlinguisticmultipleattributedecisionmakingbasedonanewcorrelationcoefficientmethodanditsapplicationinhospitalassessment AT shouzhenzeng aprobabilisticlinguisticmultipleattributedecisionmakingbasedonanewcorrelationcoefficientmethodanditsapplicationinhospitalassessment AT jichen aprobabilisticlinguisticmultipleattributedecisionmakingbasedonanewcorrelationcoefficientmethodanditsapplicationinhospitalassessment AT dandanluo probabilisticlinguisticmultipleattributedecisionmakingbasedonanewcorrelationcoefficientmethodanditsapplicationinhospitalassessment AT shouzhenzeng probabilisticlinguisticmultipleattributedecisionmakingbasedonanewcorrelationcoefficientmethodanditsapplicationinhospitalassessment AT jichen probabilisticlinguisticmultipleattributedecisionmakingbasedonanewcorrelationcoefficientmethodanditsapplicationinhospitalassessment |