Single-Valued Neutrosophic Set Correlation Coefficient and Its Application in Fault Diagnosis
Abstract
:1. Introduction
1.1. Research Status
1.2. Contribution of This Work
2. Preliminaries
2.1. Triangular Fuzzy Numbers
2.2. Single-Valued Neutrosophic Sets
3. The Proposed Method
3.1. Correlation Coefficient between Single-Valued Neutrosophic Sets
- (1)
- According to the structural symmetry of the Formula (5), the condition is satisfied.
- (2)
- For each element in the Formula (5), they are satisfied , so obviously ; The proof of inequality as follows:And because of the inequality:Therefore, we can get:Therefore:There is:Finally, contacting the previous types, there are:In summary, the condition is satisfied;
- (3)
- If , so for any , all , , , we can see from the structure of Formula (5), .
3.2. Fault Diagnosis Method
4. Illustrative Example and Discussion
4.1. Fault Diagnosis
- (i).
- According to the fault template data, the triangular fuzzy numbers under various attributes are obtained, in turn, as shown in Table 1:According to the analyzed sample data, the triangular fuzzy numbers under various attributes are obtained, in turn, as shown in Table 2:For the analyzed sample Xk ( represents the attribute), Xk and (where represent three kinds of faults) are used for matching, respectively. The neutrosophic numbers statistics generated by the determined-membership degree T, non-membership degree F, and indeterminacy-membership degree I, are calculated, as shown in Table 3:
- (ii).
- Next, for the same fault template, neutrosophic sets with different attributes under fuzzy sample X, we can get the single-valued neutrosophic decision matrix, as shown in Table 4:
- (iii).
- According to the single-valued neutrosophic set decision matrix and Formula (11) under sample X in Table 4, the ideal neutrosophic set can be obtained as follows:
- (iv).
- The weights of attributes are all the same, that is the weight matrix is as follows:Next, according to Table 4, Formula (7), (13), (14), for the fault template type () and the ideal single-valued neutrosophic set , calculate the improved weight correlation coefficient as follows:
- (v).
- Finally, according to Formula (15), , it can be seen that the analyzed samples X1-X4 belong to the first type of fault, namely, the X fault.
4.2. Fault Diagnosis Accuracy
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Min Value | Average Value | Max Value | Area | ||
---|---|---|---|---|---|
X | X11-X15 | 0.0661 | 0.1614605 | 0.2006 | 0.06725 |
X21-X25 | 0.121 | 0.149226 | 0.3468 | 0.1129 | |
X31-X35 | 0.0899 | 0.1123885 | 0.1296 | 0.01985 | |
X41-X45 | 0.357 | 4.3256515 | 4.666 | 2.1545 | |
Y | Y11-Y15 | 0.1567 | 0.181797 | 0.2038 | 0.02355 |
Y21-Y25 | 0.3071 | 0.329311 | 0.351 | 0.02195 | |
Y31-Y35 | 0.1865 | 0.242014 | 0.3218 | 0.06765 | |
Y41-Y45 | 4.094 | 4.715255 | 8.896 | 2.401 | |
Z | Z11-Z15 | 0.3006 | 0.3294004 | 0.3476 | 0.0235 |
Z21-Z25 | 0.2801 | 0.343854 | 0.3647 | 0.0423 | |
Z31-Z35 | 0.1151 | 0.136169 | 0.1864 | 0.03565 | |
Z41-Z45 | 9.385 | 9.810633 | 10.112 | 0.3635 |
Min Value | Average Value | Max Value | Area | ||
---|---|---|---|---|---|
X | X1 | 0.1416 | 0.14265 | 0.144 | 0.0012 |
X2 | 0.1028 | 0.11092 | 0.3058 | 0.1015 | |
X3 | 0.1279 | 0.133655 | 0.1378 | 0.00495 | |
X4 | 4.06 | 4.0938 | 4.18 | 0.06 |
Analyzed Sample | Fault Template | Neutrosophic Number |
---|---|---|
X1 | X11-X15 | (0.9612,0.0388,0.9914) |
Y11-Y15 | (0,1,0.6751) | |
Z11-Z15 | (0,1,0.6747) | |
X2 | X21-X25 | (0.7540,0.2460,0.6610) |
Y21-Y25 | (0,1,0.5972) | |
Z21-Z25 | (0.0126,0.9874,0.6722) | |
X3 | X31-X35 | (0.0127,0.9873,0.6451) |
Y31-Y35 | (0,1,1) | |
Z31-Z35 | (0.9836,0.0164,0.6952) | |
X4 | X41-X45 | (0.9966,0.0034,0.9348) |
Y41-Y45 | (0.0871,0.9129,0.9989) | |
Z41-Z45 | (0,1,0.5757) |
Diagnosis Fault | X1 | X2 | X3 | X4 |
---|---|---|---|---|
X11-X45 | (0.9612,0.0388,0.9914) | (0.7540,0.2460,0.6610) | (0.0127,0.9873,0.6451) | (0.9966,0.0034,0.9348) |
Y11-Y45 | (0,1,0.6751) | (0,1,0.5972) | (0,1,1) | (0.0871,0.9129,0.9989) |
Z11-Z45 | (0,1,0.6747) | (0.0126,0.9874,0.6722) | (0.9836,0.0164,0.6952) | (0,1,0.5757) |
Unknow Fault | SVNPWA | The Proposed Algorithm | ||
---|---|---|---|---|
Times of Right | Times of Error | Times of Right | Times of Error | |
X | 38 | 2 | 40 | 0 |
Y | 40 | 0 | 39 | 1 |
Z | 40 | 0 | 40 | 0 |
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Iryna, S.; Zhong, Y.; Jiang, W.; Deng, X.; Geng, J. Single-Valued Neutrosophic Set Correlation Coefficient and Its Application in Fault Diagnosis. Symmetry 2020, 12, 1371. https://doi.org/10.3390/sym12081371
Iryna S, Zhong Y, Jiang W, Deng X, Geng J. Single-Valued Neutrosophic Set Correlation Coefficient and Its Application in Fault Diagnosis. Symmetry. 2020; 12(8):1371. https://doi.org/10.3390/sym12081371
Chicago/Turabian StyleIryna, Shchur, Yu Zhong, Wen Jiang, Xinyang Deng, and Jie Geng. 2020. "Single-Valued Neutrosophic Set Correlation Coefficient and Its Application in Fault Diagnosis" Symmetry 12, no. 8: 1371. https://doi.org/10.3390/sym12081371