Figure 1.
Bird swarm algorithm pseudocode.
Figure 1.
Bird swarm algorithm pseudocode.
Figure 2.
Proposed method of the dynamic bird swarm algorithm.
Figure 2.
Proposed method of the dynamic bird swarm algorithm.
Figure 3.
Fuzzy system designed with trapezoidal MFs.
Figure 3.
Fuzzy system designed with trapezoidal MFs.
Figure 4.
Fuzzy rules proposed for the first fuzzy system.
Figure 4.
Fuzzy rules proposed for the first fuzzy system.
Figure 5.
Fuzzy rules proposed for the second fuzzy system.
Figure 5.
Fuzzy rules proposed for the second fuzzy system.
Figure 6.
Fuzzy rules proposed for the third fuzzy system.
Figure 6.
Fuzzy rules proposed for the third fuzzy system.
Figure 7.
Fuzzy rules proposed for the fourth fuzzy system.
Figure 7.
Fuzzy rules proposed for the fourth fuzzy system.
Figure 8.
Fuzzy system proposed for the dynamic parameter adaptation designed with Gaussian MFs.
Figure 8.
Fuzzy system proposed for the dynamic parameter adaptation designed with Gaussian MFs.
Figure 9.
IT2FS proposed for the parameter dynamic adaptation using trapezoidal MFs.
Figure 9.
IT2FS proposed for the parameter dynamic adaptation using trapezoidal MFs.
Figure 10.
IT2FS proposed for the parameter dynamic adaptation using Gaussian MFs.
Figure 10.
IT2FS proposed for the parameter dynamic adaptation using Gaussian MFs.
Figure 11.
DBSA applied in the optimization of fuzzy system.
Figure 11.
DBSA applied in the optimization of fuzzy system.
Figure 12.
Systolic quotient input.
Figure 12.
Systolic quotient input.
Figure 13.
Diastolic quotient input.
Figure 13.
Diastolic quotient input.
Figure 14.
Nocturnal blood pressure level output.
Figure 14.
Nocturnal blood pressure level output.
Figure 15.
Systolic quotient input.
Figure 15.
Systolic quotient input.
Figure 16.
Diastolic quotient input.
Figure 16.
Diastolic quotient input.
Figure 17.
Nocturnal blood pressure level output.
Figure 17.
Nocturnal blood pressure level output.
Figure 18.
Optimized systolic quotient input.
Figure 18.
Optimized systolic quotient input.
Figure 19.
Optimized diastolic quotient input.
Figure 19.
Optimized diastolic quotient input.
Figure 20.
Optimized nocturnal blood pressure output.
Figure 20.
Optimized nocturnal blood pressure output.
Figure 21.
Optimized systolic quotient input.
Figure 21.
Optimized systolic quotient input.
Figure 22.
Optimized diastolic quotient input.
Figure 22.
Optimized diastolic quotient input.
Figure 23.
Optimized nocturnal blood pressure level output.
Figure 23.
Optimized nocturnal blood pressure level output.
Table 1.
Nocturnal blood pressure profile classification.
Table 1.
Nocturnal blood pressure profile classification.
Profile | Percentage of Decrease | Quotient |
---|
Extreme Dipper | >20% | <0.80 |
Dipper | 10–20% | 0.80–0.90 |
Non-Dipper | <10% | 0.91–1.00 |
Riser | <0% | >1.00 |
Table 2.
Parameters used to solve the complex function of CEC2017.
Table 2.
Parameters used to solve the complex function of CEC2017.
| M | pop | dim | FQ | a1 | a2 | c1 | c2 |
---|
BSA | 1500 | 30 | 30 | 3 | 1 | 1 | 1.5 | 1.5 |
DBSA | 1500 | 30 | 30 | 3 | 1 | 1 | Dynamic | Dynamic |
Table 3.
Mathematical complex function of CEC2017.
Table 3.
Mathematical complex function of CEC2017.
| | Name Function | Fi |
---|
Unimodal Benchmark functions | 5 | Shifted and Rotated Rastrigin’s Function | 500 |
6 | Shifted and Rotated Expanded Scaffer’s F6 Function | 600 |
7 | Shifted and Rotated Lunacek Bi Rastrigin’s Function | 700 |
8 | Shifted and Rotated Non-Continuous Rastrigin’s Function | 800 |
9 | Shifted and Rotated Levy Function | 900 |
10 | Shifted and Rotated Schwefel’s Function | 1000 |
Hybrid benchmark functions | 11 | Hybrid Function 1 (N = 3) | 1100 |
Multimodal benchmark functions | 21 | Composition Function 1 (N = 3) | 2100 |
22 | Composition Function 2 (N = 3) | 2200 |
23 | Composition Function 3 (N = 4) | 2300 |
[−100, 100] |
Table 4.
Result of DBSA using type-1 fuzzy systems in CEC2017 functions.
Table 4.
Result of DBSA using type-1 fuzzy systems in CEC2017 functions.
No | Fi | Original | 1st FIS | 2nd FIS #2 | 3rd FIS | 4th FIS |
---|
Triang | Gauss | Triang | Gauss | Triang | Gauss | Triang | Gauss |
---|
5 | 500 | 8.396 × 102 | 7.529 × 102 | 7.428 × 102 | 7.404 × 102 | 7.436 × 102 | 7.569 × 102 | 7.563 × 102 | 7.359 × 102 | 7.382 × 102 |
6 | 600 | 6.732 × 102 | 6.458 × 102 | 6.456 × 102 | 6.510 × 102 | 6.518 × 102 | 6.559 × 102 | 6.563 × 102 | 6.494 × 102 | 6.491 × 102 |
7 | 700 | 1.355 × 103 | 1.082 × 103 | 1.082 × 103 | 1.093 × 103 | 1.084 × 103 | 1.125 × 103 | 1.122 × 103 | 1.070 × 103 | 1.093 × 103 |
8 | 800 | 1.075 × 103 | 1.002 × 103 | 1.002 × 103 | 9.989 × 102 | 1.005 × 103 | 1.011 × 103 | 1.013 × 103 | 9.971 × 102 | 9.925 × 102 |
9 | 900 | 7.602 × 103 | 4.100 × 103 | 4.110 × 103 | 4.310 × 103 | 4.072 × 103 | 4.825 × 103 | 4.654 × 103 | 3.775 × 103 | 4.389 × 103 |
10 | 1000 | 7.243 × 103 | 7.399 × 103 | 7.408 × 103 | 7.261 × 103 | 7.358 × 103 | 7.278 × 103 | 7.285 × 103 | 7.451 × 103 | 7.063 × 103 |
11 | 1100 | 5.349 × 103 | 6.303 × 103 | 1.791 × 103 | 1.678 × 103 | 1.784 × 103 | 1.783 × 103 | 1.780 × 103 | 1.763 × 103 | 1.580 × 103 |
21 | 2100 | 2.645 × 103 | 2.508 × 103 | 2.512 × 103 | 2.516 × 103 | 2.513 × 103 | 2.531 × 103 | 2.534 × 103 | 2.497 × 103 | 2.513 × 103 |
22 | 2200 | 8.184 × 103 | 4.513 × 103 | 4.233 × 103 | 4.230 × 103 | 4.200 × 103 | 4.376 × 103 | 4.179 × 103 | 4.328 × 103 | 4.278 × 103 |
23 | 2300 | 3.352 × 103 | 3.043 × 103 | 3.008 × 103 | 3.033 × 103 | 3.012 × 103 | 3.063 × 103 | 3.054 × 103 | 2.979 × 103 | 2.891 × 103 |
Table 5.
Result of DBSA using IT2FS in CEC2017 functions.
Table 5.
Result of DBSA using IT2FS in CEC2017 functions.
No | Fi | Original | 1st FIS | 2nd FIS | 3rd FIS | 4th FIS |
---|
Triang | Gauss | Triang | Gauss | Triang | Gauss | Triang | Gauss |
---|
5 | 500 | 8.40102 | 7.434 × 102 | 7.453 × 102 | 7.320 × 102 | 7.320 × 102 | 7.488 × 102 | 7.523 × 102 | 7.383 × 102 | 7.364 × 102 |
6 | 600 | 6.732 × 102 | 6.518 × 102 | 6.522 × 102 | 6.461 × 102 | 6.454 × 102 | 6.516 × 102 | 6.515 × 102 | 6.505 × 102 | 6.505 × 102 |
7 | 700 | 1.355 × 103 | 1.122 × 103 | 1.120 × 103 | 1.084 × 103 | 1.080 × 103 | 1.113 × 103 | 1.111 × 103 | 1.114 × 103 | 1.074 × 103 |
8 | 800 | 1.075 × 103 | 9.976 × 102 | 9.963 × 102 | 1.006 × 103 | 1.003 × 103 | 1.006 × 103 | 1.014 × 103 | 1.011 × 103 | 9.983 × 102 |
9 | 900 | 7.602 × 103 | 4.69 × 103 | 4.748 × 103 | 4.090 × 103 | 4.049 × 103 | 4.647 × 103 | 4.522 × 103 | 4.586 × 103 | 3.874 × 103 |
10 | 1000 | 7.243 × 103 | 6.916 × 103 | 6.944 × 103 | 7.372 × 103 | 7.431 × 103 | 7.245 × 103 | 7.290 × 103 | 7.263 × 103 | 7.407 × 103 |
11 | 1100 | 5.349 × 103 | 1.581 × 103 | 1.590 × 103 | 1.784 × 103 | 1.814 × 103 | 1.718 × 103 | 1.808 × 103 | 1.775 × 103 | 1.785 × 103 |
21 | 2100 | 2.645 × 103 | 2.528 × 103 | 2.526 × 103 | 2.512 × 103 | 2.504 × 103 | 2.526 × 103 | 2.528 × 103 | 2.527 × 103 | 2.500 × 103 |
22 | 2200 | 8.184 × 1003 | 4.480 × 103 | 4.596 × 103 | 4.053 × 103 | 4.236 × 103 | 4.455 × 103 | 4.250 × 103 | 4.190 × 103 | 4.315 × 103 |
23 | 2300 | 3.352 × 1003 | 3.067 × 103 | 3.064 × 103 | 3.016 × 103 | 3.000 × 103 | 3.049 × 103 | 3.042 × 103 | 3.046 × 103 | 2.987 × 103 |
Table 6.
Comparison with the HFPSO method.
Table 6.
Comparison with the HFPSO method.
Function | Min | HFPSO | Original | DBSA | DBSAT2 |
---|
Triangular | Gauss |
---|
5 | 500 | 7.43 × 102 | 8.40 × 102 | 7.359 × 102 | 7.364 × 102 |
6 | 600 | 6.54 × 102 | 6.732 × 102 | 6.494 × 102 | 6.505 × 102 |
7 | 700 | 1.063 × 103 | 1.355 × 103 | 1.070 × 103 | 1.074 × 103 |
8 | 800 | 1.017 × 103 | 1.075 × 103 | 9.971 × 102 | 9.983 × 102 |
9 | 900 | 9.04 × 103 | 7.602 × 103 | 3.775 × 103 | 3.874 × 103 |
10 | 1000 | 7.49 × 103 | 7.243 × 103 | 7.451 × 103 | 7.407 × 103 |
11 | 1100 | 2.28 × 103 | 5.349 × 103 | 1.763 × 103 | 1.785 × 103 |
21 | 2100 | 2.51 × 103 | 2.645 × 103 | 2.497 × 103 | 2.500 × 103 |
22 | 2200 | 5.80 × 103 | 8.184 × 103 | 4.328 × 103 | 4.315 × 103 |
23 | 2300 | 2.96 × 103 | 3.352 × 103 | 2.979 × 103 | 2.987 × 103 |
Table 7.
Percentage of success in each experiment.
Table 7.
Percentage of success in each experiment.
No | FISTra | FISGauss |
---|
1 | 100% | 93% |
2 | 93% | 93% |
3 | 100% | 100% |
4 | 100% | 97% |
5 | 93% | 93% |
6 | 97% | 93% |
7 | 97% | 100% |
8 | 93% | 100% |
9 | 93% | 100% |
10 | 97% | 100% |
11 | 100% | 93% |
12 | 100% | 93% |
13 | 100% | 100% |
14 | 100% | 100% |
15 | 93% | 100% |
16 | 87% | 87% |
17 | 100% | 93% |
18 | 100% | 100% |
19 | 90% | 100% |
20 | 100% | 100% |
21 | 100% | 100% |
22 | 87% | 100% |
23 | 100% | 93% |
24 | 100% | 100% |
25 | 93% | 97% |
26 | 93% | 100% |
27 | 100% | 90% |
28 | 100% | 90% |
29 | 100% | 100% |
30 | 100% | 100% |
Table 8.
Comparative of the results provided for the nocturnal blood pressure profile optimized using trapezoidal membership functions.
Table 8.
Comparative of the results provided for the nocturnal blood pressure profile optimized using trapezoidal membership functions.
No | Real Values | Non-Optimized FS | CSO | DBSA |
---|
Level | Quotient | Linguistic Output | Fuzzy Result | Linguistic Output | Fuzzy Result | Linguistic Output | Fuzzy Result |
---|
1 | ExtremeDipper | 0.76 | ExtremeDipper | 0.60 | ExtremeDipper | 0.61 | ExtremeDipper | 0.61 |
2 | Dipper | 0.89 | Dipper | 0.85 | Dipper | 0.86 | Dipper | 0.89 |
3 | Dipper | 0.81 | Dipper | 0.85 | Dipper | 0.86 | Dipper | 0.83 |
4 | Dipper | 0.82 | Dipper | 0.85 | Dipper | 0.86 | Dipper | 0.85 |
5 | No Dipper | 0.91 | Dipper | 0.85 | Dipper | 0.85 | NonDipper | 0.94 |
6 | Dipper | 0.87 | Dipper | 0.85 | Dipper | 0.86 | Dipper | 0.85 |
7 | ExtremeDipper | 0.77 | Dipper | 0.85 | Dipper | 0.85 | ExtremeDipper | 0.61 |
8 | NonDipper | 0.90 | Dipper | 0.85 | Dipper | 0.85 | NonDipper | 0.94 |
9 | NonDipper | 0.94 | NonDipper | 0.96 | NonDipper | 0.96 | NonDipper | 0.94 |
10 | Dipper | 0.83 | Dipper | 0.85 | Dipper | 0.85 | Dipper | 0.85 |
11 | NonDipper | 0.92 | Dipper | 0.85 | Dipper | 0.85 | NonDipper | 0.94 |
12 | ReverseDipper | 1.03 | ReverseDipper | 1.16 | ReverseDipper | 1.1 | ReverseDipper | 1.15 |
13 | Dipper | 0.84 | Dipper | 0.85 | Dipper | 0.86 | Dipper | 0.85 |
14 | ReverseDipper | 1.07 | ReverseDipper | 1.17 | ReverseDipper | 1.16 | ReverseDipper | 1.16 |
15 | NonDipper | 0.91 | Dipper | 0.85 | Dipper | 0.85 | NonDipper | 0.94 |
16 | Dipper | 0.82 | Dipper | 0.85 | Dipper | 0.86 | Dipper | 0.85 |
17 | Dipper | 0.86 | Dipper | 0.85 | Dipper | 0.85 | Dipper | 0.85 |
18 | NonDipper | 0.90 | Dipper | 0.85 | Dipper | 0.85 | NonDipper | 0.94 |
19 | Dipper | 0.84 | Dipper | 0.85 | Dipper | 0.85 | Dipper | 0.85 |
20 | NonDipper | 0.93 | Dipper | 0.85 | Dipper | 0.85 | NonDipper | 0.94 |
21 | NonDipper | 0.93 | NonDipper | 0.96 | NonDipper | 0.96 | NonDipper | 0.94 |
22 | Dipper | 0.83 | Dipper | 0.85 | Dipper | 0.86 | Dipper | 0.85 |
23 | NonDipper | 0.92 | NonDipper | 0.96 | NonDipper | 0.97 | NonDipper | 0.94 |
24 | ExtremeDipper | 0.72 | ExtremeDipper | 0.59 | ExtremeDipper | 0.61 | ExtremeDipper | 0.60 |
25 | Dipper | 0.85 | Dipper | 0.85 | Dipper | 0.86 | Dipper | 0.85 |
26 | Dipper | 0.89 | Dipper | 0.85 | Dipper | 0.85 | Dipper | 0.85 |
27 | Dipper | 0.89 | Dipper | 0.85 | Dipper | 0.85 | Dipper | 0.85 |
28 | NonDipper | 0.93 | NonDipper | 0.96 | NonDipper | 0.96 | NonDipper | 0.94 |
29 | NonDipper | 0.94 | NonDipper | 0.96 | NonDipper | 0.96 | NonDipper | 0.94 |
30 | Dipper | 0.83 | Dipper | 0.85 | Dipper | 0.86 | Dipper | 0.85 |
Table 9.
Comparative of the results provided for the nocturnal blood pressure profile optimized using Gaussian membership functions.
Table 9.
Comparative of the results provided for the nocturnal blood pressure profile optimized using Gaussian membership functions.
No | Real | Non-Optimized FS | CSO | DBSA |
---|
Level | Quotient | Linguistic Output | Fuzzy Result | Linguistic Output | Fuzzy Result | Linguistic Output | Fuzzy Result |
---|
1 | ExtremeDipper | 0.76 | ExtremeDipper | 0.64 | ExtremeDipper | 0.71 | ExtremeDipper | 0.61 |
2 | Dipper | 0.89 | Dipper | 0.85 | Dipper | 0.89 | Dipper | 0.89 |
3 | Dipper | 0.81 | ExtremeDipper | 0.77 | Dipper | 0.84 | Dipper | 0.83 |
4 | Dipper | 0.82 | ExtremeDipper | 0.79 | Dipper | 0.84 | Dipper | 0.85 |
5 | NonDipper | 0.91 | Dipper | 0.89 | NonDipper | 0.91 | NonDipper | 0.94 |
6 | Dipper | 0.87 | Dipper | 0.83 | Dipper | 0.87 | Dipper | 0.85 |
7 | ExtremeDipper | 0.77 | ExtremeDipper | 0.66 | ExtremeDipper | 0.78 | ExtremeDipper | 0.61 |
8 | NonDipper | 0.90 | Dipper | 0.86 | NonDipper | 0.91 | NonDipper | 0.94 |
9 | NonDipper | 0.94 | NonDipper | 0.96 | Dipper | 0.87 | NonDipper | 0.94 |
10 | Dipper | 0.83 | ExtremeDipper | 0.79 | Dipper | 0.84 | Dipper | 0.85 |
11 | NonDipper | 0.92 | NonDipper | 0.94 | NonDipper | 0.93 | NonDipper | 0.94 |
12 | ReverseDipper | 1.03 | ReverseDipper | 1.10 | ReverseDipper | 1.03 | ReverseDipper | 1.15 |
13 | Dipper | 0.84 | Dipper | 0.82 | Dipper | 0.85 | Dipper | 0.85 |
14 | ReverseDipper | 1.07 | ReverseDipper | 1.13 | ReverseDipper | 1.15 | ReverseDipper | 1.16 |
15 | NonDipper | 0.91 | NonDipper | 0.90 | Dipper | 0.86 | NonDipper | 0.94 |
16 | Dipper | 0.82 | ExtremeDipper | 0.79 | Dipper | 0.84 | Dipper | 0.85 |
17 | Dipper | 0.86 | Dipper | 0.82 | Dipper | 0.85 | Dipper | 0.85 |
18 | NonDipper | 0.90 | Dipper | 0.88 | NonDipper | 0.91 | NonDipper | 0.94 |
19 | Dipper | 0.84 | Dipper | 0.80 | Dipper | 0.85 | Dipper | 0.85 |
20 | NonDipper | 0.93 | NonDipper | 0.95 | NonDipper | 0.94 | NonDipper | 0.94 |
21 | NonDipper | 0.93 | NonDipper | 0.96 | NonDipper | 0.94 | NonDipper | 0.94 |
22 | Dipper | 0.83 | Dipper | 0.80 | Dipper | 0.84 | Dipper | 0.85 |
23 | NonDipper | 0.92 | NonDipper | 0.92 | NonDipper | 0.92 | NonDipper | 0.94 |
24 | ExtremeDipper | 0.72 | ExtremeDipper | 0.63 | ExtremeDipper | 0.61 | ExtremeDipper | 0.60 |
25 | Dipper | 0.85 | Dipper | 0.83 | Dipper | 0.85 | Dipper | 0.85 |
26 | Dipper | 0.89 | Dipper | 0.82 | Dipper | 0.89 | Dipper | 0.85 |
27 | Dipper | 0.89 | Dipper | 0.83 | Dipper | 0.89 | Dipper | 0.85 |
28 | NonDipper | 0.93 | NonDipper | 0.95 | NonDipper | 0.93 | NonDipper | 0.94 |
29 | NonDipper | 0.94 | NonDipper | 0.96 | NonDipper | 0.94 | NonDipper | 0.94 |
30 | Dipper | 0.83 | Dipper | 0.81 | Dipper | 0.85 | Dipper | 0.85 |
Table 10.
Comparative of the different optimization results.
Table 10.
Comparative of the different optimization results.
CSO | DBSA |
---|
Trapezoida_lMF | Gaussian_MF | Trapezoidal_MF | Gaussian_MF |
---|
91.46% | 87.59% | 97% | 97% |
Table 11.
Parameters used for the nocturnal blood pressure classifier design with trapezoidal membership function.
Table 11.
Parameters used for the nocturnal blood pressure classifier design with trapezoidal membership function.
Inputs and Output | MFs | Non-Optimized Parameters | Optimized Parameters |
---|
a | b | c | d | a | b | c | d |
---|
SystolicQuotient | GreaterFall | 0.4 | 0.4 | 0.6655 | 0.8 | 0.4 | 0.469 | 0.67 | 0.8166 |
Fall | 0.787 | 0.811 | 0.889 | 0.9102 | 0.7858 | 0.8232 | 0.8636 | 0.9035 |
Increase | 0.898 | 0.923 | 0.9821 | 1.02 | 0.8945 | 0.918 | 0.9684 | 1.005 |
GreaterIncrease | 1.001 | 1.09 | 1.3 | 1.3 | 1.001 | 1.09 | 1.236 | 1.3 |
DiastolicQuotient | GreaterFall | 0.4 | 0.4 | 0.6655 | 0.8 | 0.4 | 0.4366 | 0.6182 | 0.8182 |
Fall | 0.787 | 0.811 | 0.889 | 0.9102 | 0.7921 | 0.8277 | 0.8644 | 0.9117 |
Increase | 0.898 | 0.923 | 0.9821 | 1.02 | 0.87 | 0.9224 | 0.9581 | 1.006 |
GreaterIncrease | 1.004 | 1.09 | 1.3 | 1.3 | 0.972 | 1.1 | 1.27 | 1.3 |
Nocturnal blood pressure profile level | ExtremeDipper | 0.4 | 0.4 | 0.6655 | 0.8 | 0.4 | 0.456 | 0.6951 | 0.8105 |
Dipper | 0.787 | 0.811 | 0.889 | 0.9102 | 0.7972 | 0.8212 | 0.8673 | 0.9093 |
NonDipper | 0.898 | 0.923 | 0.9821 | 1.02 | 0.8822 | 0.9257 | 0.965 | 1.013 |
Riser | 1.006 | 1.09 | 1.3 | 1.3 | 0.9912 | 1.1 | 1.236 | 1.3 |
Table 12.
Parameters used for the nocturnal blood pressure classifier design with Gaussian membership function.
Table 12.
Parameters used for the nocturnal blood pressure classifier design with Gaussian membership function.
Inputs and Output | MFs | Non-Optimized Parameters | Optimized Parameters |
---|
a | b | a | b |
---|
SystolicQuotient | GreaterFall | 0.42 | 0.162 | 0.4266 | 0.1071 |
Fall | 0.82 | 0.03337 | 0.8385 | 0.02628 |
Increase | 0.957 | 0.03122 | 0.9478 | 0.02611 |
GreaterIncrease | 1.28 | 0.1236 | 1.316 | 0.1119 |
DiastolicQuotient | GreaterFall | 0.402 | 0.1854 | 0.4674 | 0.1088 |
Fall | 0.8548 | 0.0313 | 0.842 | 0.02634 |
Increase | 0.957 | 0.0315 | 0.9502 | 0.0254 |
GreaterIncrease | 1.28 | 0.1236 | 1.31 | 0.1091 |
Nocturnal blood pressure profile level | ExtremeDipper | 0.402 | 0.1854 | 0.4343 | 0.1017 |
Dipper | 0.8558 | 0.0325 | 0.8442 | 0.02911 |
NonDipper | 0.9595 | 0.0273 | 0.9371 | 0.02413 |
Riser | 1.28 | 0.1438 | 1.288 | 0.1104 |
Table 13.
Parameters used in Z-Test for DBSA vs. HFPSO.
Table 13.
Parameters used in Z-Test for DBSA vs. HFPSO.
Parameter of Z-Test for DBSA vs. HFPSO |
---|
Critical Value (Zc) | 1.64 |
Confidence interval | 95% |
H0 | µ1 ≥ µ2 |
Ha (Claim) | µ1 < µ2 |
Alpha | 0.05 |
Table 14.
Statistical test results for CEC2017 functions using type-1 fuzzy systems.
Table 14.
Statistical test results for CEC2017 functions using type-1 fuzzy systems.
Function | HFPSO | DE | DBSA FisT1 | D.E | Z Test | Evidence |
---|
5 | 7.43 × 102 | 2.83 × 101 | 7.3594 × 102 | 4.1862 × 101 | −1.384 | NS |
6 | 6.54 × 102 | 1.49 × 101 | 6.4937 × 102 | 9.9485 × 100 | −2.791 | S |
7 | 1.06 × 103 | 3.82 × 101 | 1.0695 × 103 | 5.2146 × 101 | 1.548 | NS |
8 | 1.02 × 103 | 3.49 × 101 | 9.9711 × 102 | 3.0107 × 101 | −4.991 | S |
9 | 9.04 × 103 | 2.42 × 103 | 3.7745 × 103 | 1.2676 × 103 | −19.283 | S |
10 | 7.49 × 103 | 9.11 × 102 | 7.4514 × 103 | 8.4525 × 102 | −0.322 | NS |
11 | 2.28 × 103 | 6.81 × 102 | 1.7630 × 103 | 2.2155 × 102 | −7.25 | S |
21 | 2.51 × 103 | 2.92 × 105 | 2.4966 × 103 | 3.3743 × 101 | 0 | NS |
22 | 5.80 × 103 | 3.26 × 101 | 4.3283 × 103 | 2.5558 × 103 | −5.742 | S |
23 | 2.96 × 103 | 7.41 × 101 | 2.9792 × 103 | 1.0784 × 102 | 1.527 | NS |
Table 15.
Statistical test results for CEC2017 functions using IT2FS.
Table 15.
Statistical test results for CEC2017 functions using IT2FS.
Function | HFPSO | DE | DBSA FisT2 | D.E | Z Test | Evidence |
---|
5 | 7.43 × 102 | 2.83 × 101 | 7.364 × 102 | 3.930 × 101 | −1.445 | NS |
6 | 6.54 × 102 | 1.49 × 101 | 6.505 × 102 | 1.040 × 101 | −1.651 | S |
7 | 1.06 × 103 | 3.82 × 101 | 1.074 × 103 | 5.390 × 101 | 1.514 | NS |
8 | 1.02 × 103 | 3.49 × 101 | 9.983 × 102 | 2.850 × 101 | −4.883 | S |
9 | 9.04 × 103 | 2.42 × 103 | 3.874 × 103 | 1.310 × 103 | −18.788 | S |
10 | 7.49 × 103 | 9.11 × 102 | 7.407 × 103 | 8.413 × 102 | −0.645 | NS |
11 | 2.28 × 103 | 6.81 × 102 | 1.785 × 103 | 3.203 × 102 | −6.512 | S |
21 | 2.51 × 103 | 2.92 × 105 | 2.500 × 103 | 3.570 × 101 | 0 | NS |
22 | 5.80 × 103 | 3.26 × 101 | 4.315 × 103 | 2.580 × 103 | −5.775 | S |
23 | 2.96 × 103 | 7.41 × 101 | 2.987 × 103 | 1.010 × 102 | 2.395 | NS |
Table 16.
Parameters used in Z-Test for DBSA vs. CSO.
Table 16.
Parameters used in Z-Test for DBSA vs. CSO.
Parameters of Z-Test for DBSA vs. CSO |
---|
Critical Value (Zc) | 1.645 |
Confidential interval | 95% |
H0 | µ1 ≤ µ2 |
Ha (Claim) | µ1 > µ2 |
Alpha | 0.05 |
Table 17.
Z-test descriptive statistics.
Table 17.
Z-test descriptive statistics.
Var | Obs | Mean | S. D |
---|
DBSA | 30 | 97 | 0.1213 |
CSO | 30 | 91.458 | 1.944 |
Table 18.
Z-test results.
Table 18.
Z-test results.
Z | 15.607 |
p-value | 0 |
α | 0.05 |
Zc | 1.645 |
Table 19.
Z-test descriptive statistics.
Table 19.
Z-test descriptive statistics.
Var | Obs | Mean | S. D |
---|
DBSA | 30 | 97 | 0.1161 |
CSO | 30 | 87.50 | 2.390 |
Table 20.
Z-test results.
Table 20.
Z-test results.
Z | 21.746 |
p-value | 0 |
α | 0.05 |
Zc | 1.645 |
Table 21.
ANOVA comparing results of trapezoidal MFs.
Table 21.
ANOVA comparing results of trapezoidal MFs.
Source of Variance | SS | df | MS | F | p-Value | F Critic |
---|
Between groups | 422.68 | 1 | 422.68 | 37.43 | 8.71 × 10−8 | 4.01 |
Within Groups | 655.00 | 58 | 11.29 | | | |
Total | 1077.68 | 59 | | | | |
Table 22.
ANOVA comparing results of Gaussian MFs.
Table 22.
ANOVA comparing results of Gaussian MFs.
Source of Variance | SS | df | MS | F | p-Value | F Critic |
---|
Between groups | 1306.67 | 1 | 1306.67 | 117.72 | 1.39 × 10−15 | 4.01 |
Within Groups | 643.79 | 58 | 11.10 | | | |
Total | 1950.46 | 59 | | | | |