Improved Symmetry Measures of Simplified Neutrosophic Sets and Their Decision-Making Method Based on a Sine Entropy Weight Model
This work indicates the insufficiency of existing symmetry measures (SMs) between asymmetry measures of simplified neutrosophic sets (SNSs) and proposes the improved normalized SMs of SNSs, including the improved SMs and weighted SMs in single-valued and interval neutrosophic settings. Then, the sin...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-06-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/6/225 |
| _version_ | 1798034688560857088 |
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| author | Wenhua Cui Jun Ye |
| author_facet | Wenhua Cui Jun Ye |
| author_sort | Wenhua Cui |
| collection | DOAJ |
| description | This work indicates the insufficiency of existing symmetry measures (SMs) between asymmetry measures of simplified neutrosophic sets (SNSs) and proposes the improved normalized SMs of SNSs, including the improved SMs and weighted SMs in single-valued and interval neutrosophic settings. Then, the sine entropy measures of SNSs are presented to establish a sine entropy weight model for solving the criteria weights in decision-making. Based on the improved weighted SMs of SNSs and the sine entropy weight model, a multi-criteria decision-making (MCDM) method with unknown criteria weights (an improved MCDM method) is established in the SNS setting. In the MCDM process, corresponding to the criteria weights obtained by the sine entropy model, the ranking order of all alternatives and the best one are given by means of the improved weighted SMs between the ideal solution and each alternative. Lastly, the improved MCDM method is applied to an actual decision example in single-valued and interval neutrosophic settings to indicate the feasibility of the improved MCDM method. By comparative analysis with existing MCDM methods, the improved SMs and the sine entropy weight model not only provide a simpler and more effective method for MCDM problems with unknown criteria weights in the SNS setting, but can also overcome the insufficiency of the existing SMs and MCDM method. |
| first_indexed | 2024-04-11T20:47:42Z |
| format | Article |
| id | doaj.art-ee6cf4fb59d247b492bf47b18bb076bc |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T20:47:42Z |
| publishDate | 2018-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ee6cf4fb59d247b492bf47b18bb076bc2022-12-22T04:03:58ZengMDPI AGSymmetry2073-89942018-06-0110622510.3390/sym10060225sym10060225Improved Symmetry Measures of Simplified Neutrosophic Sets and Their Decision-Making Method Based on a Sine Entropy Weight ModelWenhua Cui0Jun Ye1Department of Electrical Engineering and Automation, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, ChinaDepartment of Electrical Engineering and Automation, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, ChinaThis work indicates the insufficiency of existing symmetry measures (SMs) between asymmetry measures of simplified neutrosophic sets (SNSs) and proposes the improved normalized SMs of SNSs, including the improved SMs and weighted SMs in single-valued and interval neutrosophic settings. Then, the sine entropy measures of SNSs are presented to establish a sine entropy weight model for solving the criteria weights in decision-making. Based on the improved weighted SMs of SNSs and the sine entropy weight model, a multi-criteria decision-making (MCDM) method with unknown criteria weights (an improved MCDM method) is established in the SNS setting. In the MCDM process, corresponding to the criteria weights obtained by the sine entropy model, the ranking order of all alternatives and the best one are given by means of the improved weighted SMs between the ideal solution and each alternative. Lastly, the improved MCDM method is applied to an actual decision example in single-valued and interval neutrosophic settings to indicate the feasibility of the improved MCDM method. By comparative analysis with existing MCDM methods, the improved SMs and the sine entropy weight model not only provide a simpler and more effective method for MCDM problems with unknown criteria weights in the SNS setting, but can also overcome the insufficiency of the existing SMs and MCDM method.http://www.mdpi.com/2073-8994/10/6/225simplified neutrosophic symmetry measuresine entropyinterval neutrosophic setsingle-valued neutrosophic setdecision making |
| spellingShingle | Wenhua Cui Jun Ye Improved Symmetry Measures of Simplified Neutrosophic Sets and Their Decision-Making Method Based on a Sine Entropy Weight Model Symmetry simplified neutrosophic symmetry measure sine entropy interval neutrosophic set single-valued neutrosophic set decision making |
| title | Improved Symmetry Measures of Simplified Neutrosophic Sets and Their Decision-Making Method Based on a Sine Entropy Weight Model |
| title_full | Improved Symmetry Measures of Simplified Neutrosophic Sets and Their Decision-Making Method Based on a Sine Entropy Weight Model |
| title_fullStr | Improved Symmetry Measures of Simplified Neutrosophic Sets and Their Decision-Making Method Based on a Sine Entropy Weight Model |
| title_full_unstemmed | Improved Symmetry Measures of Simplified Neutrosophic Sets and Their Decision-Making Method Based on a Sine Entropy Weight Model |
| title_short | Improved Symmetry Measures of Simplified Neutrosophic Sets and Their Decision-Making Method Based on a Sine Entropy Weight Model |
| title_sort | improved symmetry measures of simplified neutrosophic sets and their decision making method based on a sine entropy weight model |
| topic | simplified neutrosophic symmetry measure sine entropy interval neutrosophic set single-valued neutrosophic set decision making |
| url | http://www.mdpi.com/2073-8994/10/6/225 |
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