A Novel q-Rung Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Entropy Weights
Abstract
:1. Introduction
2. Literature Review
3. Preliminaries
3.1. The q-Rung Dual Hesitant Fuzzy Sets
- (1)
- ;
- (2)
- ;
- (3)
- ;
- (4)
- .
- (1)
- If , then ;
- (2)
- If , thenif , then ;if , then ;
- (1)
- ;
- (2)
- if and only if ;
- (3)
- .
3.2. PA, HM and PHM Operators
- (1)
- (2)
- ;
- (3)
- , if .
4. Some Aggregation Operators and Their Properties
4.1. The q-Rung Dual Hesitant Fuzzy Power Hamy Mean Operator
- (1)
- ;
- (2)
- ;
- (3)
- , if , and is the distance between and .
4.2. The q-Rung Dual Hesitant Fuzzy Power Weighted Hamy Mean Operator
5. A Method to Determine the Attribute Weights Based on Entropy
- (1)
- , if and only if or;
- (2)
- , if and only if and, where and are the ith smallest values of and, respectively;
- (3)
- if,
- (4)
6. A Novel MADM Method Based on q-RDHFEs
7. Assessment Indicator System of Hospital Medical Quality
7.1. Analysis Evaluation Factors from the Perspective of Patients
7.1.1. Work Efficiency
- (1)
- Utilization rate of hospital beds. It can reflect the ratio between the total number of beds used per day and the total number of existing beds, and reflect the load of hospital beds. In addition, high utilization rate indicates that the use of hospital beds is scientific and reasonable.
- (2)
- Average length of hospital stay. The average hospital stay represents the average length of stay of each discharged patient within a period, which is a comprehensive index for estimating hospital efficiency, medical quality, and technical level.
- (3)
- The number of outpatient and emergency patients received by each employee per day. It can reflect the work efficiency of the hospital staff.
7.1.2. Medical Quality
- (1)
- Cure rate, improvement rate and mortality rate. These indicators are the link quality indicators in the clinical quality evaluation. The patient’s cure status truly reflects the hospital’s medical quality.
- (2)
- Success rate of critically ill rescue. The rescue success rate of critically ill patients not only reflects the medical quality of the hospital and the technical level of medical staff, but also represents the management level of a hospital.
- (3)
- Satisfaction of nursing service. The patient’s satisfaction with the nursing service of medical staff will affect the doctor-patient relationship and the patient’s satisfaction with the hospital.
7.1.3. Workload
- (1)
- Number of visits. The number of visits is the general term for the total number of visits to the hospital for treatment, including emergency and outpatient.
- (2)
- Number of hospitalizations. In general, there is a certain relationship between the number of visits to the hospital and the number of hospitalizations. As the number of visits increases, the number of hospitalizations also increases. Both of these indicators have an impact on the evaluation of hospital workload.
7.2. Establish Medical Quality Evaluation System and Decision Matrix
7.3. The Decision-Making Process
7.4. Analysis of the Impact of Parameters
7.4.1. The Influence of the Parameter q on the Results
7.4.2. The Influence of the Parameter k on the Results
7.5. Validity Analysis
7.5.1. Compared with Xu et al.’s Method
7.5.2. Compared with Wei et al.’s Method
7.5.3. Compared with Zhang et al.’s Method
7.6. Advantages of Our Method
7.6.1. It Can Effectively Deal with DMs’ Unreasonable Evaluation Values
7.6.2. It Can Determine the Weight Information of Attributes Objectively
7.6.3. It Can Consider the Complex Interrelationship among Multiple Attributes
7.6.4. It Can Effectively Express DM’s Evaluation Comprehensively
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. The Proof Process of Theory 1 in Section 3.1
Appendix B. The Proof Process of Theory 2 in Section 3.1
Appendix C. The Proof Process of Theory 3 in Section 3.1
Appendix D. The Proof Process of Theory 4 in Section 3.2
Appendix E. The Proof Process of Theory 5 in Section 3.2
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References | Theory | Characteristics |
---|---|---|
Fuzzy Sets | ||
Zadeh [27] (1965) | FSs | The MD is interval [0, 1]. |
Atanassov [28] (1986) | IFSs | The sum of MD and NMD should be less than or equal to one. |
Torra [30] (2010) | HFSs | The MD is denoted by a set of possible values in [0, 1]. |
Zhu et al. [19] (2012) | DHFSs | The sum of maximum values of MD and NMD is less than or equal to one. |
Yager [29] (2014) | PFSs | The square sum of MD and NMD is less than or equal to one. |
Yager [18] (2017) | q-ROFSs | The sum of the qth power of MD and the qth power of NMD does not exceed 1. |
Xu et al. [17] (2018) | q-RDHFSs | Both MD and NMD are denoted by multiple values and the sum of qth power of maximum MD and qth power of maximum NMD does not exceed 1. |
Aggregation Operators | ||
Bonferroni [15] (1950) | BM | It considers the interrelationship among any two arguments. |
Sykora [16] (2009) | HEM | It considers the interrelationship among any two arguments. |
Yager [37] (2001) | PA | It effectively handles extreme input arguments. |
He et al. [38] (2014) | PBM | It takes the advantages of PA and BM. |
Peide Liu [39] (2017) | PHEM | It takes the advantages of PA and HEM. |
Hara et al. [46] (1998) | HM | It can consider the interrelationship among multiple arguments. |
Peide Liu [47] (2019) | PHM | It takes the advantages of PA and HM. |
Index | Implication |
---|---|
Work efficiency (C1) | Utilization rate of hospital beds |
Average length of hospital stay | |
The number of outpatient emergency patients | |
Medical quality (C2) | Cure rate, improvement rate and case fatality rate |
Success rate of critically ill rescue | |
Satisfaction of nursing service | |
Workload (C3) | Number of visits |
Number of hospitalizations |
C1 | C2 | C3 | |
---|---|---|---|
A1 | |||
A2 | |||
A3 | |||
A4 |
q | Ranking Orders | |
---|---|---|
q = 1 | ,, , | |
q = 2 | ,, ,4 | |
q = 3 | ,, , | |
q = 4 | ,, , | |
q = 5 | ,, , |
k | Ranking Orders | |
---|---|---|
k = 1 | ,, , | |
k = 2 | ,, , | |
k = 3 | ,, , |
Methods | Ranking Orders | |
---|---|---|
Xu et al.’s [17] method based on q-RDHFWHM operator (t = 1, s = 1, q = 3) | ,, , | |
Our method based on q-RDHFPWHM (k = 1, q = 3) | ,, , |
Methods | Ranking Orders | |
---|---|---|
Wei et al.’s [54] method based on DHPFHWA operator | ,, , | |
Our method based on q-RDHFPWHM (k = 3, q = 2) | ,, , |
C1 | C2 | C3 | C4 | |
---|---|---|---|---|
A1 | ||||
A2 | ||||
A3 | ||||
A4 | ||||
A5 |
Methods | Ranking Orders | |
---|---|---|
Zhang’s [55] method based on DHFMSM operator | ,, ,, | |
Our method based on q-RDHFPWHM (k = 3, q = 2) | ,, ,, |
Methods | Ranking Orders | |
---|---|---|
Zhang et al.’s [55] method based on DHFMSM operator (k = 2) | ,, ,, | |
Our method based on q-RDHFPWHM (k = 2, q = 3) | ,, ,, |
k | Ranking Orders | |
---|---|---|
k = 1 | ,, ,, | |
k = 2 | ,, ,, | |
k = 3 | ,, ,, | |
k = 4 | ,, ,, |
Method | Ranking Orders | |
---|---|---|
Zhang’s [55] method based on DHFMSM operator | Cannot be calculated | —— |
Our method based on q-RDHFPWHM(k = 2; q = 5) | ,, , , |
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Kou, Y.; Feng, X.; Wang, J. A Novel q-Rung Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Entropy Weights. Entropy 2021, 23, 1322. https://doi.org/10.3390/e23101322
Kou Y, Feng X, Wang J. A Novel q-Rung Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Entropy Weights. Entropy. 2021; 23(10):1322. https://doi.org/10.3390/e23101322
Chicago/Turabian StyleKou, Yaqing, Xue Feng, and Jun Wang. 2021. "A Novel q-Rung Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Entropy Weights" Entropy 23, no. 10: 1322. https://doi.org/10.3390/e23101322