Approaches to Three-Way Decisions Based on the Evaluation of Probabilistic Linguistic Terms Sets
The method of determining probability thresholds of three-way decisions (3WDs) has always been the key of research, especially in the current environment with a large number of data and uncertainties. Among these problems, there will be correlation and similarity between them. In the light of these...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/5/764 |
| _version_ | 1797535897098387456 |
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| author | Pingping Gu Jiubing Liu Xianzhong Zhou |
| author_facet | Pingping Gu Jiubing Liu Xianzhong Zhou |
| author_sort | Pingping Gu |
| collection | DOAJ |
| description | The method of determining probability thresholds of three-way decisions (3WDs) has always been the key of research, especially in the current environment with a large number of data and uncertainties. Among these problems, there will be correlation and similarity between them. In the light of these problems, the loss function with Probabilistic Linguistic Terms Sets (PLTSs) is introduced in the paper, and then we propose a PLTS evaluation-based approach to determine the thresholds and derive 3WDs. According to the definition and characters of PLTSs, the PLTSs loss function matrix is constructed firstly. Then using the equivalent model of Decision-theoretic rough sets (DTRSs), we construct the equivalent model (i.e., the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>α</mi><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow></msup></semantics></math></inline-formula>-model and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>β</mi><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow></msup></semantics></math></inline-formula>-model, which are symmtrical) and try to find the optimal solution to determine the thresholds. Based on that, we propose a novel three-way decision approach under PLTSs evaluations. Finally, the validity of the method is verified by an example. |
| first_indexed | 2024-03-10T11:51:53Z |
| format | Article |
| id | doaj.art-2eaaec46ba2a4d33bf4abecfa712e39c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T11:51:53Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2eaaec46ba2a4d33bf4abecfa712e39c2023-11-21T17:36:22ZengMDPI AGSymmetry2073-89942021-04-0113576410.3390/sym13050764Approaches to Three-Way Decisions Based on the Evaluation of Probabilistic Linguistic Terms SetsPingping Gu0Jiubing Liu1Xianzhong Zhou2School of Management and Engineering, Nanjing University, Nanjing 210023, ChinaSchool of Business, Shantou University, Shantou 515063, ChinaSchool of Management and Engineering, Nanjing University, Nanjing 210023, ChinaThe method of determining probability thresholds of three-way decisions (3WDs) has always been the key of research, especially in the current environment with a large number of data and uncertainties. Among these problems, there will be correlation and similarity between them. In the light of these problems, the loss function with Probabilistic Linguistic Terms Sets (PLTSs) is introduced in the paper, and then we propose a PLTS evaluation-based approach to determine the thresholds and derive 3WDs. According to the definition and characters of PLTSs, the PLTSs loss function matrix is constructed firstly. Then using the equivalent model of Decision-theoretic rough sets (DTRSs), we construct the equivalent model (i.e., the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>α</mi><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow></msup></semantics></math></inline-formula>-model and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>β</mi><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow></msup></semantics></math></inline-formula>-model, which are symmtrical) and try to find the optimal solution to determine the thresholds. Based on that, we propose a novel three-way decision approach under PLTSs evaluations. Finally, the validity of the method is verified by an example.https://www.mdpi.com/2073-8994/13/5/764three-way decisionsprobability thresholdsprobabilistic linguistic terms setsequivalent model |
| spellingShingle | Pingping Gu Jiubing Liu Xianzhong Zhou Approaches to Three-Way Decisions Based on the Evaluation of Probabilistic Linguistic Terms Sets Symmetry three-way decisions probability thresholds probabilistic linguistic terms sets equivalent model |
| title | Approaches to Three-Way Decisions Based on the Evaluation of Probabilistic Linguistic Terms Sets |
| title_full | Approaches to Three-Way Decisions Based on the Evaluation of Probabilistic Linguistic Terms Sets |
| title_fullStr | Approaches to Three-Way Decisions Based on the Evaluation of Probabilistic Linguistic Terms Sets |
| title_full_unstemmed | Approaches to Three-Way Decisions Based on the Evaluation of Probabilistic Linguistic Terms Sets |
| title_short | Approaches to Three-Way Decisions Based on the Evaluation of Probabilistic Linguistic Terms Sets |
| title_sort | approaches to three way decisions based on the evaluation of probabilistic linguistic terms sets |
| topic | three-way decisions probability thresholds probabilistic linguistic terms sets equivalent model |
| url | https://www.mdpi.com/2073-8994/13/5/764 |
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