Comparative Study of Type-1 and Interval Type-2 Fuzzy Logic Systems in Parameter Adaptation for the Fuzzy Discrete Mycorrhiza Optimization Algorithm
Abstract
:1. Introduction
2. Optimization
3. Fuzzy Logic Systems
Interval Type-2 Fuzzy Logic System
4. Related Work
- Foraging for light, water, and other nutrients;
- The ability to defend themselves against herbivores and other attackers;
- The ability to “remember” past events.
- Light (phototropism), plants constantly monitor their visible environment.
- Gravity (geotropism), the plant’s root network also moves, and the root tips respond to gravity.
- Water (hydrotropism), which is the response of plant growth to water.
- Touch (thigmotropism), many plants respond to the sense of touch, such as the tendrils of climbing plants, vines, or bindweed.
5. Proposed Method
- There is communication among plants, which may or may not be of the same species, through a fungal network (MN).
- There is an exchange of resources among plants through the fungal network (MN).
- There is a defense behavior against predators that can be insects or animals, for the survival of the whole habitat (plants and fungi).
- The colonization of a forest through a fungal network (MN) thrives much more than in a forest where there is no exchange of resources (see Figure 4).
Algorithm 1: Fuzzy Discrete Mycorrhiza Optimization Algorithm (FDMOA) |
1: Objective min or max f(x), x = (x1, x2,…, xd) 2: Define parameters (a, b, c, d, e, f, x, y) 3: Initialize a population of n plants and mycorrhiza with random solutions 4: Find the best solution fit in the initial population 5: while (t < maxIter) 6: for i = 1:n (for n plants and Mycorrhiza population) 7: 8: 9: end for 10: 11: 12: Apply (LV-Cooperative Model) 13: 14: 15: if 16: 17: else 18: 19: end if 20: rand ([1 2]) 21: if (rand = 1) 22: Apply (LV-Predator-Prey Model) 23: 24: 25: else 26: Apply (LV-Competitive Model) 27: 28: 29: end if 30: Evaluate new solutions. 31: T1FLS-IT2FLS Architecture 32: Evaluate Error 33: Error minor? 34: Update T1FLS-IT2FLS Architecture. 35: Find the current best FLS-Architecture solution. 36: end while |
5.1. Discrete Mycorrhiza Optimization Algorithm
5.2. Discrete Lotka–Volterra System Equation
5.3. FDMOA Parameters
5.4. FDMOA Pseudocode
5.5. FDMOA Flowchart
5.6. Mathematical Functions
6. Results
6.1. Hypothesis Test
6.2. Discussion of Results
6.3. Programming Environment
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Description | Value |
---|---|---|
DMOA—Parameters: | ||
Population x at time t | ||
Population y at time t | ||
Grow rates of populations x at time t | ||
Grow rates of populations y at time t | ||
t | time | |
a | Population growth rate x | 0.01 |
b | Influence of population x on itself | 0.02 |
g | Influence of population y on population x | 0.06 |
d | Population growth rate y | 0 |
e | Influence of population x on population y | 1.7 |
h | Influence of population y on itself | 0.09 |
x | Initial population in x | 0.0002 |
y | Initial population in y | 0.0006 |
In the absence of population x = 0, In the absence of population y = 0 | ||
a, b, c, d, e and f—are positive constants | ||
Population | Population size | 20 |
Populations | Number of populations | 2 |
Dimensions | Dimensions size | 30, 50, 100 |
Epochs | Number of epochs | 30 |
Iterations | Iteration’s size | 30, 50, 100, 500 |
F | Function | Range | Nature |
---|---|---|---|
F1 | Sphere | [−5.12, 5.12] | U |
F2 | Rosenbrock | [−5, 10] | U |
F3 | Griewank | [−600, 600] | M |
F4 | Rastrigin | [−5.12, 5.12] | M |
F5 | Ackley | [−32.768, 32.768] | M |
F6 | Dixon-Price | [−10, 10] | U |
F7 | Michalewicz | [0, π] | M |
F8 | Powell | [−4, 5] | U |
F9 | RHE: Rotate Hyper Ellipsoid | [−65.536, 65.536] | U |
F10 | Shwefel | [−500, 500] | M |
F11 | Styblinski–Tang | [−5, 5] | U |
F12 | SDP: Sum Different Powers | [−1, 1] | M |
F13 | Sum Squares | [−10, 10] | U |
F14 | Trid | [−d2, d2] | U |
F15 | Zakharov | [−5, 10] | U |
F16 | Bukin No 6 | [−15, −5] | U |
F17 | Cross-in-Tray | [−10, 10] | M |
F18 | Drop-Wave | [−5.12. 5.12] | M |
F19 | Eggholder | [−5.12, 5.12] | M |
F20 | Beale | [−4.5, 4.5] | U |
F21 | Holder Table | [−10, 10] | M |
F22 | Branin | [−5, 10] | M |
F23 | Levy | [−10, 10] | M |
F24 | Levy 13 | [−10, 10] | M |
F25 | Schaffer 2 | [−100, 100] | M |
F26 | Schaffer 4 | [−100, 100] | M |
F27 | Shubert | [−10, 10] | M |
F28 | Bohachevsky 1 | [−100, 100] | M |
F29 | Bohachevsky 2 | [−100, 100] | M |
F30 | Bohachevsky 3 | [−100, 100] | M |
F31 | Booth | [−10, 10] | U |
F32 | Matyas | [−10, 10] | U |
F33 | Mccormick | [−1.5, 4] | U |
F34 | Easom | [−100, 100] | U |
F35 | Goldstein–Price | [−2, 2] | M |
F36 | Three-Hump Camel | [−5, 5] | M |
U | Unimodal | ||
M | Multimodal |
N | Rules If Then |
---|---|
1 | if (iter is Low) then (xi is High) |
2 | if (iter is Medium) then (xi is Medium) |
3 | if (iter is High) then (xi is Low) |
T1FLS = “fisGau318” | [System] |
Name = “fisGau318” | |
Type = “mamdani” | |
Version = 2.0 | |
NumInputs = 1 | |
NumOutputs = 1 | |
NumRules = 3 | |
AndMethod = “min” | |
OrMethod = “max” | |
ImpMethod = “min” | |
AggMethod = “max” | |
DefuzzMethod = “centroid” | |
IT2FLS = “it2_3gausS6523” | [System] |
Name = “it2_3gausS6523” | |
Type = “mamdani” | |
Version = 2.0 | |
NumInputs = 1 | |
NumOutputs = 1 | |
NumRules = 3 | |
AndMethod = “min” | |
OrMethod = “max” | |
ImpMethod = “min” | |
AggMethod = “max” | |
DefuzzMethod = “centroid” |
N | T1FLS-DMOAx30 | T1FLS-DMOAx50 | T1FLS-DMOAx100 | |||
---|---|---|---|---|---|---|
Mean | SD | Mean | SD | Mean | SD | |
1 | 1.04 × 10−12 | 2.82 × 10−12 | 1.30 × 10−12 | 3.49 × 10−12 | 3.86 × 10−12 | 1.66 × 10−11 |
2 | 2.91 × 10−15 | 6.07 × 10−15 | 7.96 × 10−16 | 2.01 × 10−15 | 7.39 × 10−15 | 2.63 × 10−14 |
3 | 5.62 × 10−17 | 2.12 × 10−16 | 1.90 × 10−16 | 5.43 × 10−16 | 3.01 × 10−14 | 8.31 × 10−14 |
4 | 1.64 × 10−12 | 4.37 × 10−12 | 8.02 × 10−13 | 1.60 × 10−12 | 8.71 × 10−13 | 3.38 × 10−12 |
5 | 2.14 × 10−9 | 1.79 × 10−9 | 2.48 × 10−9 | 1.35 × 10−8 | 1.93 × 10−8 | 1.30 × 10−8 |
6 | 7.54 × 10−13 | 1.88 × 10−12 | 1.47 × 10−12 | 3.39 × 10−12 | 7.90 × 10−13 | 2.03 × 10−12 |
7 | 2.63 × 10−13 | 4.95 × 10−13 | 1.46 × 10−12 | 4.47 × 10−12 | 2.13 × 10−12 | 6.74 × 10−12 |
8 | 2.39 × 10−13 | 6.15 × 10−13 | 1.45 × 10−12 | 4.24 × 10−12 | 8.91 × 10−13 | 2.71 × 10−12 |
9 | 8.35 × 10−13 | 2.23 × 10−12 | 1.01 × 10−12 | 2.80 × 10−12 | 5.46 × 10−13 | 1.17 × 10−12 |
10 | 1.14 × 10−12 | 3.03 × 10−12 | 9.81 × 10−13 | 2.42 × 10−12 | 9.03 × 10−13 | 1.97 × 10−12 |
11 | 5.77 × 10−13 | 1.16 × 10−12 | 4.46 × 10−13 | 7.81 × 10−13 | 1.22 × 10−12 | 3.91 × 10−12 |
12 | 7.45 × 10−13 | 1.58 × 10−12 | 6.76 × 10−15 | 1.34 × 10−14 | 2.71 × 10−20 | 7.10 × 10−20 |
13 | 1.15 × 10−12 | 3.55 × 10−12 | 1.48 × 10−12 | 3.89 × 10−12 | 2.11 × 10−12 | 5.48 × 10−12 |
14 | 4.96 × 10−13 | 1.20 × 10−12 | 1.99 × 10−12 | 7.02 × 10−12 | 4.24 × 10−13 | 8.07 × 10−13 |
15 | 5.46 × 10−13 | 1.12 × 10−12 | 4.11 × 10−13 | 9.33 × 10−13 | 1.28 × 10−13 | 2.52 × 10−13 |
16 | 6.03 × 10−13 | 1.28 × 10−12 | 5.79 × 10−13 | 1.11 × 10−12 | 5.58 × 10−13 | 1.19 × 10−12 |
17 | 1.62 × 10−15 | 3.07 × 10−15 | 5.12 × 10−16 | 8.36 × 10−16 | 4.69 × 10−16 | 1.66 × 10−15 |
18 | 4.31 × 10−17 | 9.02 × 10−17 | 1.46 × 10−16 | 3.83 × 10−16 | 8.38 × 10−17 | 2.94 × 10−16 |
19 | 6.38 × 10−13 | 1.80 × 10−12 | 4.32 × 10−12 | 1.65 × 10−11 | 9.12 × 10−13 | 1.68 × 10−12 |
20 | 2.66 × 10−12 | 6.49 × 10−12 | 7.51 × 10−13 | 1.86 × 10−12 | 7.58 × 10−13 | 1.62 × 10−12 |
21 | 1.46 × 10−12 | 7.82 × 10−12 | 4.73 × 10−13 | 2.32 × 10−12 | 2.98 × 10−14 | 6.60 × 10−14 |
22 | 1.47 × 10−12 | 2.63 × 10−12 | 8.50 × 10−13 | 3.52 × 10−12 | 1.09 × 10−12 | 3.49 × 10−12 |
23 | 1.30 × 10−12 | 3.46 × 10−12 | 5.72 × 10−13 | 1.03 × 10−12 | 3.76 × 10−13 | 8.72 × 10−13 |
24 | 6.63 × 10−13 | 1.39 × 10−12 | 3.60 × 10−12 | 1.83 × 10−11 | 2.26 × 10−12 | 7.21 × 10−12 |
25 | 1.65 × 10−15 | 5.19 × 10−15 | 1.43 × 10−15 | 4.36 × 10−15 | 6.01 × 10−16 | 1.50 × 10−15 |
26 | 2.40 × 10−8 | 1.36 × 10−8 | 1.79 × 10−8 | 1.05 × 10−8 | 1.87 × 10−8 | 9.88 × 10−9 |
27 | 1.57 × 10−13 | 2.55 × 10−13 | 3.87 × 10−13 | 8.95 × 10−13 | 2.11 × 10−12 | 7.50 × 10−12 |
28 | 3.95 × 10−13 | 9.97 × 10−13 | 4.16 × 10−13 | 8.78 × 10−13 | 4.11 × 10−12 | 9.48 × 10−12 |
29 | 2.18 × 10−12 | 6.80 × 10−12 | 2.97 × 10−13 | 6.44 × 10−13 | 6.45 × 10−13 | 1.02 × 10−12 |
30 | 1.56 × 10−12 | 3.32 × 10−12 | 4.08 × 10−13 | 7.22 × 10−13 | 2.99 × 10−13 | 5.03 × 10−13 |
31 | 1.61 × 10−12 | 3.89 × 10−12 | 2.99 × 10−12 | 1.13 × 10−11 | 9.34 × 10−13 | 2.65 × 10−12 |
32 | 1.37 × 10−12 | 3.30 × 10−12 | 1.67 × 10−13 | 4.69 × 10−13 | 1.71 × 10−13 | 5.44 × 10−13 |
33 | 2.32 × 10−12 | 6.87 × 10−12 | 1.76 × 10−12 | 4.06 × 10−12 | 1.33 × 10−12 | 3.02 × 10−12 |
34 | 1.09 × 10−20 | 3.96 × 10−20 | 3.74 × 10−20 | 1.16 × 10−19 | 5.56 × 10−20 | 2.29 × 10−19 |
35 | 1.79 × 10−12 | 5.13 × 10−12 | 3.83 × 10−13 | 7.54 × 10−13 | 4.14 × 10−13 | 8.86 × 10−13 |
36 | 1.25 × 10−12 | 3.25 × 10−12 | 6.11 × 10−13 | 1.02 × 10−12 | 1.55 × 10−12 | 4.83 × 10−12 |
N | IT2FLS-DMOAx30 | IT2FLS-DMOAx50 | IT2FLS-DMOAx100 | |||
---|---|---|---|---|---|---|
Mean | SD | Mean | SD | Mean | SD | |
1 | 5.39 × 10−20 | 1.18 × 10−19 | 3.76 × 10−20 | 9.84 × 10−20 | 3.97 × 10−20 | 6.97 × 10−20 |
2 | 9.69 × 10−22 | 2.04 × 10−21 | 7.56 × 10−22 | 9.99 × 10−22 | 7.99 × 10−22 | 1.81 × 10−21 |
3 | 1.02 × 10−22 | 2.36 × 10−22 | 1.81 × 10−22 | 4.36 × 10−22 | 6.00 × 10−21 | 1.10 × 10−20 |
4 | 3.27 × 10−20 | 6.48 × 10−20 | 4.19 × 10−20 | 8.97 × 10−20 | 6.70 × 10−20 | 1.42 × 10−19 |
5 | 1.79 × 10−18 | 1.30 × 10−18 | 2.80 × 10−18 | 5.28 × 10−18 | 6.42 × 10−18 | 4.23 × 10−18 |
6 | 1.75 × 10−20 | 4.76 × 10−20 | 2.80 × 10−20 | 3.96 × 10−20 | 5.60 × 10−20 | 7.87 × 10−20 |
7 | 2.57 × 10−20 | 3.54 × 10−20 | 5.97 × 10−20 | 1.20 × 10−19 | 6.67 × 10−20 | 2.76 × 10−19 |
8 | 2.08 × 10−20 | 4.94 × 10−20 | 7.59 × 10−20 | 2.55 × 10−19 | 5.84 × 10−20 | 1.36 × 10−19 |
9 | 2.51 × 10−20 | 6.85 × 10−20 | 4.39 × 10−20 | 7.03 × 10−20 | 3.56 × 10−20 | 6.70 × 10−20 |
10 | 3.24 × 10−20 | 6.93 × 10−20 | 4.86 × 10−20 | 8.13 × 10−20 | 3.56 × 10−20 | 6.07 × 10−20 |
11 | 8.33 × 10−20 | 1.64 × 10−19 | 4.14 × 10−20 | 6.42 × 10−20 | 6.20 × 10−20 | 8.90 × 10−20 |
12 | 2.89 × 10−20 | 4.59 × 10−20 | 1.64 × 10−20 | 5.89 × 10−20 | 6.23 × 10−24 | 4.84 × 10−24 |
13 | 1.25 × 10−20 | 1.78 × 10−20 | 5.64 × 10−20 | 9.65 × 10−20 | 1.70 × 10−20 | 2.93 × 10−20 |
14 | 4.10 × 10−20 | 7.01 × 10−20 | 2.63 × 10−20 | 4.20 × 10−20 | 3.15 × 10−20 | 6.48 × 10−20 |
15 | 3.07 × 10−20 | 4.41 × 10−20 | 2.63 × 10−20 | 4.71 × 10−20 | 4.77 × 10−20 | 8.87 × 10−20 |
16 | 2.01 × 10−20 | 5.14 × 10−20 | 2.11 × 10−20 | 2.65 × 10−20 | 2.86 × 10−20 | 3.96 × 10−20 |
17 | 7.19 × 10−22 | 1.03 × 10−21 | 1.06 × 10−21 | 1.78 × 10−21 | 8.02 × 10−22 | 1.53 × 10−21 |
18 | 2.19 × 10−22 | 5.72 × 10−22 | 1.78 × 10−22 | 7.21 × 10−22 | 5.96 × 10−23 | 1.08 × 10−22 |
19 | 3.19 × 10−20 | 6.17 × 10−20 | 2.90 × 10−20 | 5.45 × 10−20 | 3.73 × 10−20 | 4.39 × 10−20 |
20 | 3.29 × 10−20 | 5.28 × 10−20 | 3.47 × 10−20 | 5.03 × 10−20 | 2.33 × 10−20 | 3.70 × 10−20 |
21 | 1.37 × 10−20 | 4.70 × 10−20 | 6.02 × 10−21 | 1.12 × 10−20 | 1.78 × 10−20 | 4.97 × 10−20 |
22 | 4.76 × 10−20 | 1.54 × 10−19 | 6.65 × 10−20 | 1.92 × 10−19 | 1.49 × 10−20 | 2.85 × 10−20 |
23 | 1.82 × 10−20 | 3.14 × 10−20 | 1.05 × 10−19 | 1.74 × 10−19 | 1.84 × 10−20 | 3.05 × 10−20 |
24 | 3.25 × 10−20 | 6.89 × 10−20 | 3.34 × 10−20 | 6.81 × 10−20 | 2.24 × 10−20 | 4.26 × 10−20 |
25 | 9.69 × 10−22 | 2.29 × 10−21 | 9.72 × 10−22 | 2.36 × 10−21 | 3.30 × 10−22 | 6.23 × 10−22 |
26 | 6.05 × 10−18 | 4.05 × 10−18 | 7.26 × 10−18 | 5.36 × 10−18 | 7.70 × 10−18 | 5.55 × 10−18 |
27 | 7.03 × 10−20 | 1.14 × 10−19 | 4.36 × 10−20 | 8.94 × 10−20 | 1.53 × 10−20 | 2.38 × 10−20 |
28 | 5.67 × 10−20 | 1.09 × 10−19 | 4.68 × 10−20 | 1.01 × 10−19 | 4.93 × 10−20 | 8.81 × 10−20 |
29 | 4.76 × 10−20 | 9.85 × 10−20 | 3.95 × 10−20 | 6.92 × 10−20 | 3.25 × 10−20 | 5.28 × 10−20 |
30 | 3.38 × 10−20 | 6.08 × 10−20 | 3.06 × 10−20 | 6.69 × 10−20 | 2.19 × 10−20 | 4.23 × 10−20 |
31 | 6.30 × 10−20 | 7.13 × 10−20 | 5.60 × 10−20 | 1.23 × 10−19 | 2.12 × 10−20 | 3.97 × 10−20 |
32 | 2.71 × 10−20 | 6.28 × 10−20 | 4.81 × 10−20 | 9.99 × 10−20 | 2.56 × 10−20 | 4.14 × 10−20 |
33 | 4.24 × 10−20 | 8.03 × 10−20 | 2.74 × 10−20 | 4.33 × 10−20 | 2.55 × 10−20 | 3.25 × 10−20 |
34 | 4.68 × 10−24 | 2.31 × 10−24 | 6.08 × 10−24 | 3.46 × 10−24 | 4.96 × 10−24 | 2.05 × 10−24 |
35 | 2.81 × 10−20 | 4.92 × 10−20 | 2.64 × 10−20 | 3.01 × 10−20 | 1.23 × 10−19 | 3.19 × 10−19 |
36 | 9.93 × 10−20 | 2.71 × 10−19 | 6.27 × 10−20 | 1.32 × 10−19 | 2.53 × 10−20 | 4.93 × 10−20 |
T1FLS | IT2FLS | Hypothesis Test | ||||
---|---|---|---|---|---|---|
No | fisGau318 30 | it2_3gausS01 30 | ||||
Mean | SD | Mean | SD | Z | E | |
1 | 1.04 × 10−12 | 2.82 × 10−12 | 1.44 × 10−12 | 4.82 × 10−12 | −0.94 | N |
2 | 2.91 × 10−15 | 6.07 × 10−15 | 2.93 × 10−15 | 7.79 × 10−15 | −2.08 | Y |
3 | 5.62 × 10−17 | 2.12 × 10−16 | 5.54 × 10−16 | 2.08 × 10−15 | 1.96 | N |
4 | 1.64 × 10−12 | 4.37 × 10−12 | 2.83 × 10−12 | 1.09 × 10−11 | −0.99 | N |
5 | 2.14 × 10−9 | 1.79 × 10−9 | 1.14 × 10−9 | 1.08 × 10−9 | −2.8 | Y |
6 | 7.54 × 10−13 | 1.88 × 10−12 | 2.47 × 10−13 | 5.68 × 10−13 | −0.04 | N |
7 | 2.63 × 10−13 | 4.95 × 10−13 | 1.46 × 10−12 | 5.09 × 10−12 | 1.62 | N |
8 | 2.39 × 10−13 | 6.15 × 10−13 | 5.53 × 10−13 | 2.02 × 10−12 | 0.77 | N |
9 | 8.35 × 10−13 | 2.23 × 10−12 | 4.85 × 10−13 | 1.16 × 10−12 | −0.35 | N |
10 | 1.14 × 10−12 | 3.03 × 10−12 | 3.49 × 10−13 | 6.59 × 10−13 | 0.09 | N |
11 | 5.77 × 10−13 | 1.16 × 10−12 | 1.20 × 10−12 | 3.45 × 10−12 | 0.29 | N |
12 | 7.45 × 10−13 | 1.58 × 10−12 | 9.57 × 10−13 | 3.18 × 10−12 | −0.31 | N |
13 | 1.15 × 10−12 | 3.55 × 10−12 | 6.23 × 10−13 | 2.15 × 10−12 | −0.84 | N |
14 | 4.96 × 10−13 | 1.20 × 10−12 | 2.39 × 10−13 | 4.22 × 10−13 | 1.54 | N |
15 | 5.46 × 10−13 | 1.12 × 10−12 | 2.30 × 10−13 | 3.98 × 10−13 | 1.15 | N |
16 | 6.03 × 10−13 | 1.28 × 10−12 | 8.31 × 10−13 | 2.34 × 10−12 | 0.92 | N |
17 | 1.62 × 10−15 | 3.07 × 10−15 | 3.09 × 10−15 | 1.38 × 10−14 | 0.63 | N |
18 | 4.31 × 10−17 | 9.02 × 10−17 | 9.31 × 10−16 | 3.65 × 10−15 | 1.47 | N |
19 | 6.38 × 10−13 | 1.80 × 10−12 | 3.87 × 10−13 | 7.05 × 10−13 | −1.15 | N |
20 | 2.66 × 10−12 | 6.49 × 10−12 | 3.41 × 10−13 | 6.03 × 10−13 | −1.1 | N |
21 | 1.46 × 10−12 | 7.82 × 10−12 | 1.97 × 10−14 | 3.75 × 10−14 | −0.96 | N |
22 | 1.47 × 10−12 | 2.63 × 10−12 | 2.22 × 10−12 | 9.69 × 10−12 | −2.15 | Y |
23 | 1.30 × 10−12 | 3.46 × 10−12 | 8.46 × 10−13 | 2.37 × 10−12 | 0.78 | N |
24 | 6.63 × 10−13 | 1.39 × 10−12 | 9.68 × 10−13 | 3.02 × 10−12 | 0.69 | N |
25 | 1.65 × 10−15 | 5.19 × 10−15 | 1.79 × 10−15 | 7.18 × 10−15 | −0.68 | N |
26 | 2.40 × 10−8 | 1.36 × 10−8 | 1.44 × 10−8 | 7.47 × 10−9 | −3.81 | Y |
27 | 1.57 × 10−13 | 2.55 × 10−13 | 3.18 × 10−13 | 7.86 × 10−13 | −0.24 | N |
28 | 3.95 × 10−13 | 9.97 × 10−13 | 1.13 × 10−13 | 1.47 × 10−13 | −0.66 | N |
29 | 2.18 × 10−12 | 6.80 × 10−12 | 2.05 × 10−12 | 5.11 × 10−12 | −1.61 | N |
30 | 1.56 × 10−12 | 3.32 × 10−12 | 1.37 × 10−12 | 3.86 × 10−12 | −1.97 | Y |
31 | 1.61 × 10−12 | 3.89 × 10−12 | 2.26 × 10−13 | 4.34 × 10−13 | −0.07 | N |
32 | 1.37 × 10−12 | 3.30 × 10−12 | 4.40 × 10−13 | 1.22 × 10−12 | −1.25 | N |
33 | 2.32 × 10−12 | 6.87 × 10−12 | 1.45 × 10−12 | 6.94 × 10−12 | −0.97 | N |
34 | 1.09 × 10−2⁰ | 3.96 × 10−2⁰ | 2.25 × 10−2⁰ | 6.20 × 10−2⁰ | 0.98 | N |
35 | 1.79 × 10−12 | 5.13 × 10−12 | 3.85 × 10−13 | 5.53 × 10−13 | −1.1 | N |
36 | 1.25 × 10−12 | 3.25 × 10−12 | 4.75 × 10−13 | 1.30 × 10−12 | −1.31 | N |
T1DMOA | |||||
---|---|---|---|---|---|
N | Rosenbrock | Griewank | Rastrigin | Ackley | Dixon |
1 | 2.36 × 10−14 | 1.16 × 10−15 | 2.02 × 10−11 | 6.60 × 10−9 | 8.45 × 10−12 |
2 | 1.70 × 10−14 | 1.84 × 10−16 | 1.30 × 10−11 | 6.38 × 10−9 | 6.47 × 10−12 |
3 | 1.43 × 10−14 | 1.32 × 10−16 | 6.56 × 10−12 | 5.63 × 10−9 | 1.57 × 10−12 |
4 | 1.39 × 10−14 | 7.92 × 10−17 | 2.57 × 10−12 | 5.20 × 10−9 | 8.69 × 10−13 |
5 | 7.44 × 10−15 | 6.08 × 10−17 | 1.40 × 10−12 | 4.58 × 10−9 | 7.23 × 10−13 |
6 | 3.49 × 10−15 | 1.79 × 10−17 | 1.11 × 10−12 | 3.00 × 10−9 | 6.88 × 10−13 |
7 | 2.25 × 10−15 | 1.35 × 10−17 | 8.16 × 10−13 | 2.82 × 10−9 | 6.56 × 10−13 |
8 | 2.07 × 10−15 | 1.13 × 10−17 | 7.81 × 10−13 | 2.52 × 10−9 | 5.66 × 10−13 |
9 | 1.23 × 10−15 | 8.50 × 10−18 | 6.32 × 10−13 | 2.50 × 10−9 | 5.20 × 10−13 |
10 | 4.85 × 10−16 | 6.81 × 10−18 | 6.01 × 10−13 | 2.05 × 10−9 | 5.07 × 10−13 |
11 | 3.92 × 10−16 | 4.42 × 10−18 | 3.02 × 10−13 | 1.99 × 10−9 | 3.95 × 10−13 |
12 | 3.77 × 10−16 | 3.11 × 10−18 | 2.84 × 10−13 | 1.96 × 10−9 | 3.30 × 10−13 |
13 | 2.16 × 10−16 | 1.56 × 10−18 | 2.63 × 10−13 | 1.94 × 10−9 | 1.80 × 10−13 |
14 | 1.38 × 10−16 | 1.19 × 10−18 | 2.48 × 10−13 | 1.78 × 10−9 | 1.63 × 10−13 |
15 | 1.07 × 10−16 | 8.77 × 10−19 | 9.11 × 10−14 | 1.70 × 10−9 | 9.61 × 10−14 |
16 | 8.13 × 10−17 | 7.96 × 10−19 | 7.89 × 10−14 | 1.52 × 10−9 | 9.49 × 10−14 |
17 | 8.07 × 10−17 | 5.67 × 10−19 | 6.61 × 10−14 | 1.41 × 10−9 | 9.39 × 10−14 |
18 | 7.83 × 10−17 | 3.79 × 10−19 | 4.30 × 10−14 | 1.32 × 10−9 | 8.95 × 10−14 |
19 | 6.97 × 10−17 | 3.46 × 10−19 | 2.72 × 10−14 | 1.21 × 10−9 | 5.51 × 10−14 |
20 | 6.69 × 10−17 | 2.09 × 10−19 | 2.01 × 10−14 | 1.14 × 10−9 | 5.21 × 10−14 |
21 | 3.75 × 10−17 | 1.90 × 10−19 | 2.01 × 10−14 | 1.10 × 10−9 | 1.50 × 10−14 |
22 | 1.67 × 10−17 | 1.63 × 10−19 | 8.26 × 10−15 | 1.01 × 10−9 | 1.12 × 10−14 |
23 | 1.63 × 10−17 | 1.62 × 10−19 | 3.35 × 10−15 | 9.97 × 10−10 | 9.05 × 10−15 |
24 | 5.22 × 10−18 | 1.09 × 10−19 | 2.88 × 10−15 | 9.87 × 10−10 | 8.08 × 10−15 |
25 | 1.13 × 10−19 | 5.59 × 10−20 | 2.81 × 10−15 | 9.40 × 10−10 | 7.59 × 10−15 |
26 | 9.94 × 10−20 | 4.94 × 10−20 | 7.21 × 10−16 | 6.83 × 10−10 | 1.19 × 10−16 |
27 | 4.94 × 10−20 | 1.37 × 10−20 | 5.87 × 10−16 | 5.36 × 10−10 | 8.47 × 10−17 |
28 | 2.38 × 10−20 | 5.92 × 10−21 | 3.10 × 10−16 | 5.13 × 10−10 | 3.28 × 10−17 |
29 | 5.52 × 10−22 | 2.01 × 10−21 | 6.27 × 10−18 | 2.08 × 10−10 | 2.82 × 10−18 |
30 | 2.18 × 10−22 | 1.90 × 10−21 | 9.69 × 10−21 | 2.35 × 10−16 | 5.76 × 10−20 |
IT2DMOA | |||||
---|---|---|---|---|---|
N | Rosenbrock | Griewank | Rastrigin | Ackley | Dixon |
1 | 1.10 × 10−20 | 1.15 × 10−21 | 3.30 × 10−19 | 7.33 × 10−18 | 2.56 × 10−19 |
2 | 2.53 × 10−21 | 6.51 × 10−22 | 1.50 × 10−19 | 3.44 × 10−18 | 7.39 × 10−20 |
3 | 2.14 × 10−21 | 2.49 × 10−22 | 8.57 × 10−20 | 3.18 × 10−18 | 3.87 × 10−20 |
4 | 1.89 × 10−21 | 1.92 × 10−22 | 7.09 × 10−20 | 2.91 × 10−18 | 3.20 × 10−20 |
5 | 1.73 × 10−21 | 1.79 × 10−22 | 5.33 × 10−20 | 2.70 × 10−18 | 2.72 × 10−20 |
6 | 1.60 × 10−21 | 1.40 × 10−22 | 4.24 × 10−20 | 2.56 × 10−18 | 1.75 × 10−20 |
7 | 1.57 × 10−21 | 7.15 × 10−23 | 4.15 × 10−20 | 2.41 × 10−18 | 1.53 × 10−20 |
8 | 1.33 × 10−21 | 5.31 × 10−23 | 3.40 × 10−20 | 2.07 × 10−18 | 1.00 × 10−20 |
9 | 1.29 × 10−21 | 4.75 × 10−23 | 2.41 × 10−20 | 2.03 × 10−18 | 8.16 × 10−21 |
10 | 9.88 × 10−22 | 3.73 × 10−23 | 2.26 × 10−20 | 1.86 × 10−18 | 7.74 × 10−21 |
11 | 7.09 × 10−22 | 3.61 × 10−23 | 2.03 × 10−20 | 1.81 × 10−18 | 6.86 × 10−21 |
12 | 6.90 × 10−22 | 3.13 × 10−23 | 1.34 × 10−20 | 1.62 × 10−18 | 5.37 × 10−21 |
13 | 4.46 × 10−22 | 2.70 × 10−23 | 1.16 × 10−20 | 1.55 × 10−18 | 4.83 × 10−21 |
14 | 2.83 × 10−22 | 2.62 × 10−23 | 1.08 × 10−20 | 1.48 × 10−18 | 4.62 × 10−21 |
15 | 2.25 × 10−22 | 2.54 × 10−23 | 1.04 × 10−20 | 1.45 × 10−18 | 4.03 × 10−21 |
16 | 1.82 × 10−22 | 2.31 × 10−23 | 9.73 × 10−21 | 1.43 × 10−18 | 3.72 × 10−21 |
17 | 1.47 × 10−22 | 2.04 × 10−23 | 8.79 × 10−21 | 1.41 × 10−18 | 2.84 × 10−21 |
18 | 9.52 × 10−23 | 1.97 × 10−23 | 6.98 × 10−21 | 1.35 × 10−18 | 2.63 × 10−21 |
19 | 8.76 × 10−23 | 1.95 × 10−23 | 6.55 × 10−21 | 1.33 × 10−18 | 1.62 × 10−21 |
20 | 5.84 × 10−23 | 1.23 × 10−23 | 5.24 × 10−21 | 1.26 × 10−18 | 1.16 × 10−21 |
21 | 3.47 × 10−23 | 7.12 × 10−24 | 4.86 × 10−21 | 1.26 × 10−18 | 1.14 × 10−21 |
22 | 3.12 × 10−23 | 5.57 × 10−24 | 4.16 × 10−21 | 1.13 × 10−18 | 5.58 × 10−22 |
23 | 3.05 × 10−23 | 5.30 × 10−24 | 3.13 × 10−21 | 1.05 × 10−18 | 2.14 × 10−22 |
24 | 9.22 × 10−24 | 4.56 × 10−24 | 3.07 × 10−21 | 1.03 × 10−18 | 1.80 × 10−22 |
25 | 5.51 × 10−24 | 3.73 × 10−24 | 2.86 × 10−21 | 9.60 × 10−19 | 8.63 × 10−23 |
26 | 4.24 × 10−24 | 3.27 × 10−24 | 2.07 × 10−21 | 8.09 × 10−19 | 7.28 × 10−23 |
27 | 2.44 × 10−24 | 2.50 × 10−24 | 1.64 × 10−21 | 7.61 × 10−19 | 3.99 × 10−23 |
28 | 3.98 × 10−25 | 2.49 × 10−24 | 5.63 × 10−22 | 7.07 × 10−19 | 2.67 × 10−23 |
29 | 1.39 × 10−25 | 1.04 × 10−24 | 2.11 × 10−22 | 6.77 × 10−19 | 1.28 × 10−23 |
30 | 4.22 × 10−26 | 1.17 × 10−25 | 1.96 × 10−22 | 1.88 × 10−19 | 6.05 × 10−24 |
No | T1FLS | IT2FLS | Hypothesis Test | |||
---|---|---|---|---|---|---|
fisGau318 30 | it2_3gausS6523 30 | |||||
Mean | SD | Mean | SD | Z | E | |
1 | 1.04 × 10−12 | 2.82 × 10−12 | 5.39 × 10−20 | 1.18 × 10−19 | −2.12 | Y |
2 | 2.91 × 10−15 | 6.07 × 10−15 | 9.69 × 10−22 | 2.04 × 10−21 | −2.76 | Y |
3 | 5.62 × 10−17 | 2.12 × 10−16 | 1.02 × 10−22 | 2.36 × 10−22 | −1.52 | N |
4 | 1.64 × 10−12 | 4.37 × 10−12 | 3.27 × 10−20 | 6.48 × 10−20 | −2.16 | Y |
5 | 2.14 × 10−9 | 1.79 × 10−9 | 1.79 × 10−18 | 1.30 × 10−18 | −6.88 | Y |
6 | 7.54 × 10−13 | 1.88 × 10−12 | 1.75 × 10−20 | 4.76 × 10−20 | −2.31 | Y |
7 | 2.63 × 10−13 | 4.95 × 10−13 | 2.57 × 10−20 | 3.54 × 10−20 | −3.06 | Y |
8 | 2.39 × 10−13 | 6.15 × 10−13 | 2.08 × 10−20 | 4.94 × 10−20 | −2.24 | Y |
9 | 8.35 × 10−13 | 2.23 × 10−12 | 2.51 × 10−20 | 6.85 × 10−20 | −2.16 | Y |
10 | 1.14 × 10−12 | 3.03 × 10−12 | 3.24 × 10−20 | 6.93 × 10−20 | −2.16 | Y |
11 | 5.77 × 10−13 | 1.16 × 10−12 | 8.33 × 10−20 | 1.64 × 10−19 | −2.86 | Y |
12 | 7.45 × 10−13 | 1.58 × 10−12 | 2.89 × 10−20 | 4.59 × 10−20 | −2.72 | Y |
13 | 1.15 × 10−12 | 3.55 × 10−12 | 1.25 × 10−20 | 1.78 × 10−20 | −1.86 | Y |
14 | 4.96 × 10−13 | 1.20 × 10−12 | 4.10 × 10−20 | 7.01 × 10−20 | −2.37 | Y |
15 | 5.46 × 10−13 | 1.12 × 10−12 | 3.07 × 10−20 | 4.41 × 10−20 | −2.8 | Y |
16 | 6.03 × 10−13 | 1.28 × 10−12 | 2.01 × 10−20 | 5.14 × 10−20 | −2.71 | Y |
17 | 1.62 × 10−15 | 3.07 × 10−15 | 7.19 × 10−22 | 1.03 × 10−21 | −3.03 | Y |
18 | 4.31 × 10−17 | 9.02 × 10−17 | 2.19 × 10−22 | 5.72 × 10−22 | −2.75 | Y |
19 | 6.38 × 10−13 | 1.80 × 10−12 | 3.19 × 10−20 | 6.17 × 10−20 | −2.03 | Y |
20 | 2.66 × 10−12 | 6.49 × 10−12 | 3.29 × 10−20 | 5.28 × 10−20 | −2.36 | Y |
21 | 1.46 × 10−12 | 7.82 × 10−12 | 1.37 × 10−20 | 4.70 × 10−20 | −1.07 | N |
22 | 1.47 × 10−12 | 2.63 × 10−12 | 4.76 × 10−20 | 1.54 × 10−19 | −3.22 | Y |
23 | 1.30 × 10−12 | 3.46 × 10−12 | 1.82 × 10−20 | 3.14 × 10−20 | −2.15 | Y |
24 | 6.63 × 10−13 | 1.39 × 10−12 | 3.25 × 10−20 | 6.89 × 10−20 | −2.74 | Y |
25 | 1.65 × 10−15 | 5.19 × 10−15 | 9.69 × 10−22 | 2.29 × 10−21 | −1.82 | Y |
26 | 2.40 × 10−8 | 1.36 × 10−8 | 6.05 × 10−18 | 4.05 × 10−18 | −10.17 | Y |
27 | 1.57 × 10−13 | 2.55 × 10−13 | 7.03 × 10−20 | 1.14 × 10−19 | −3.54 | Y |
28 | 3.95 × 10−13 | 9.97 × 10−13 | 5.67 × 10−20 | 1.09 × 10−19 | −2.28 | Y |
29 | 2.18 × 10−12 | 6.80 × 10−12 | 4.76 × 10−20 | 9.85 × 10−20 | −1.84 | Y |
30 | 1.56 × 10−12 | 3.32 × 10−12 | 3.38 × 10−20 | 6.08 × 10−20 | −2.7 | Y |
31 | 1.61 × 10−12 | 3.89 × 10−12 | 6.30 × 10−20 | 7.13 × 10−20 | −2.38 | Y |
32 | 1.37 × 10−12 | 3.30 × 10−12 | 2.71 × 10−20 | 6.28 × 10−20 | −2.39 | Y |
33 | 2.32 × 10−12 | 6.87 × 10−12 | 4.24 × 10−20 | 8.03 × 10−20 | −1.94 | Y |
34 | 1.09 × 10−20 | 3.96 × 10−20 | 4.68 × 10−24 | 2.31 × 10−24 | −1.58 | N |
35 | 1.79 × 10−12 | 5.13 × 10−12 | 2.81 × 10−20 | 4.92 × 10−20 | −2.01 | Y |
36 | 1.25 × 10−12 | 3.25 × 10−12 | 9.93 × 10−20 | 2.71 × 10−19 | −2.22 | Y |
33 |
T1FLS | IT2FLS | Hypothesis Test | ||||
---|---|---|---|---|---|---|
No | fisGau318 50 | it2_3gausS6523 50 | ||||
Mean | SD | Mean | SD | Z | E | |
1 | 1.30 × 10−12 | 3.49 × 10−12 | 3.76 × 10−20 | 9.84 × 10−20 | −2.04 | Y |
2 | 7.96 × 10−16 | 2.01 × 10−15 | 7.56 × 10−22 | 9.99 × 10−22 | −2.17 | Y |
3 | 1.90 × 10−16 | 5.43 × 10−16 | 1.81 × 10−22 | 4.36 × 10−22 | −1.92 | Y |
4 | 8.02 × 10−13 | 1.60 × 10−12 | 4.19 × 10−20 | 8.97 × 10−20 | −2.74 | Y |
5 | 2.48 × 10−9 | 1.35 × 10−8 | 2.80 × 10−18 | 5.28 × 10−18 | −1 | N |
6 | 1.47 × 10−12 | 3.39 × 10−12 | 2.80 × 10−20 | 3.96 × 10−20 | −2.38 | Y |
7 | 1.46 × 10−12 | 4.47 × 10−12 | 5.97 × 10−20 | 1.20 × 10−19 | −1.78 | Y |
8 | 1.45 × 10−12 | 4.24 × 10−12 | 7.59 × 10−20 | 2.55 × 10−19 | −1.88 | Y |
9 | 1.01 × 10−12 | 2.80 × 10−12 | 4.39 × 10−20 | 7.03 × 10−20 | −1.97 | Y |
10 | 9.81 × 10−13 | 2.42 × 10−12 | 4.86 × 10−20 | 8.13 × 10−20 | −2.22 | Y |
11 | 4.46 × 10−13 | 7.81 × 10−13 | 4.14 × 10−20 | 6.42 × 10−20 | −3.13 | Y |
12 | 6.76 × 10−15 | 1.34 × 10−14 | 1.64 × 10−20 | 5.89 × 10−20 | −2.76 | Y |
13 | 1.48 × 10−12 | 3.89 × 10−12 | 5.64 × 10−20 | 9.65 × 10−20 | −2.09 | Y |
14 | 1.99 × 10−12 | 7.02 × 10−12 | 2.63 × 10−20 | 4.20 × 10−20 | −1.55 | N |
15 | 4.11 × 10−13 | 9.33 × 10−13 | 2.63 × 10−20 | 4.71 × 10−20 | −2.41 | Y |
16 | 5.79 × 10−13 | 1.11 × 10−12 | 2.11 × 10−20 | 2.65 × 10−20 | −2.87 | Y |
17 | 5.12 × 10−16 | 8.36 × 10−16 | 1.06 × 10−21 | 1.78 × 10−21 | −3.36 | Y |
18 | 1.46 × 10−16 | 3.83 × 10−16 | 1.78 × 10−22 | 7.21 × 10−22 | −2.09 | Y |
19 | 4.32 × 10−12 | 1.65 × 10−11 | 2.90 × 10−20 | 5.45 × 10−20 | −1.44 | N |
20 | 7.51 × 10−13 | 1.86 × 10−12 | 3.47 × 10−20 | 5.03 × 10−20 | −2.21 | Y |
21 | 4.73 × 10−13 | 2.32 × 10−12 | 6.02 × 10−21 | 1.12 × 10−20 | −1.12 | N |
22 | 8.50 × 10−13 | 3.52 × 10−12 | 6.65 × 10−20 | 1.92 × 10−19 | −1.32 | N |
23 | 5.72 × 10−13 | 1.03 × 10−12 | 1.05 × 10−19 | 1.74 × 10−19 | −3.06 | Y |
24 | 3.60 × 10−12 | 1.83 × 10−11 | 3.34 × 10−20 | 6.81 × 10−20 | −1.08 | N |
25 | 1.43 × 10−15 | 4.36 × 10−15 | 9.72 × 10−22 | 2.36 × 10−21 | −1.8 | Y |
26 | 1.79 × 10−8 | 1.05 × 10−8 | 7.26 × 10−18 | 5.36 × 10−18 | −9.35 | Y |
27 | 3.87 × 10−13 | 8.95 × 10−13 | 4.36 × 10−20 | 8.94 × 10−20 | −2.37 | Y |
28 | 4.16 × 10−13 | 8.78 × 10−13 | 4.68 × 10−20 | 1.01 × 10−19 | −2.6 | Y |
29 | 2.97 × 10−13 | 6.44 × 10−13 | 3.95 × 10−20 | 6.92 × 10−20 | −2.53 | Y |
30 | 4.08 × 10−13 | 7.22 × 10−13 | 3.06 × 10−20 | 6.69 × 10−20 | −3.09 | Y |
31 | 2.99 × 10−12 | 1.13 × 10−11 | 5.60 × 10−20 | 1.23 × 10−19 | −1.46 | N |
32 | 1.67 × 10−13 | 4.69 × 10−13 | 4.81 × 10−20 | 9.99 × 10−20 | −1.95 | Y |
33 | 1.76 × 10−12 | 4.06 × 10−12 | 2.74 × 10−20 | 4.33 × 10−20 | −2.37 | Y |
34 | 3.74 × 10−20 | 1.16 × 10−19 | 6.08 × 10−24 | 3.46 × 10−24 | −1.76 | Y |
35 | 3.83 × 10−13 | 7.54 × 10−13 | 2.64 × 10−20 | 3.01 × 10−20 | −2.78 | Y |
36 | 6.11 × 10−13 | 1.02 × 10−12 | 6.27 × 10−20 | 1.32 × 10−19 | −3.27 | Y |
29 |
T1FLS | IT2FLS | Hypothesis Test | ||||
---|---|---|---|---|---|---|
No | fisGau318 100 | it2_3gausS6523 100 | ||||
Mean | SD | Mean | SD | Z | E | |
1 | 3.86 × 10−12 | 1.66 × 10−11 | 3.97 × 10−20 | 6.97 × 10−20 | −1.27 | N |
2 | 7.39 × 10−15 | 2.63 × 10−14 | 7.99 × 10−22 | 1.81 × 10−21 | −1.54 | N |
3 | 3.01 × 10−14 | 8.31 × 10−14 | 6.00 × 10−21 | 1.10 × 10−20 | −1.98 | Y |
4 | 8.71 × 10−13 | 3.38 × 10−12 | 6.70 × 10−20 | 1.42 × 10−19 | −1.41 | N |
5 | 1.93 × 10−8 | 1.30 × 10−8 | 6.42 × 10−18 | 4.23 × 10−18 | −8.11 | Y |
6 | 7.90 × 10−13 | 2.03 × 10−12 | 5.60 × 10−20 | 7.87 × 10−20 | −2.13 | Y |
7 | 2.13 × 10−12 | 6.74 × 10−12 | 6.67 × 10−20 | 2.76 × 10−19 | −1.73 | Y |
8 | 8.91 × 10−13 | 2.71 × 10−12 | 5.84 × 10−20 | 1.36 × 10−19 | −1.8 | Y |
9 | 5.46 × 10−13 | 1.17 × 10−12 | 3.56 × 10−20 | 6.70 × 10−20 | −2.55 | Y |
10 | 9.03 × 10−13 | 1.97 × 10−12 | 3.56 × 10−20 | 6.07 × 10−20 | −2.51 | Y |
11 | 1.22 × 10−12 | 3.91 × 10−12 | 6.20 × 10−20 | 8.90 × 10−20 | −1.71 | Y |
12 | 2.71 × 10−20 | 7.10 × 10−20 | 6.23 × 10−24 | 4.84 × 10−24 | −2.09 | Y |
13 | 2.11 × 10−12 | 5.48 × 10−12 | 1.70 × 10−20 | 2.93 × 10−20 | −2.11 | Y |
14 | 4.24 × 10−13 | 8.07 × 10−13 | 3.15 × 10−20 | 6.48 × 10−20 | −2.88 | Y |
15 | 1.28 × 10−13 | 2.52 × 10−13 | 4.77 × 10−20 | 8.87 × 10−20 | −2.78 | Y |
16 | 5.58 × 10−13 | 1.19 × 10−12 | 2.86 × 10−20 | 3.96 × 10−20 | −2.57 | Y |
17 | 4.69 × 10−16 | 1.66 × 10−15 | 8.02 × 10−22 | 1.53 × 10−21 | −1.54 | N |
18 | 8.38 × 10−17 | 2.94 × 10−16 | 5.96 × 10−23 | 1.08 × 10−22 | −1.56 | N |
19 | 9.12 × 10−13 | 1.68 × 10−12 | 3.73 × 10−20 | 4.39 × 10−20 | −2.98 | Y |
20 | 7.58 × 10−13 | 1.62 × 10−12 | 2.33 × 10−20 | 3.70 × 10−20 | −2.57 | Y |
21 | 2.98 × 10−14 | 6.60 × 10−14 | 1.78 × 10−20 | 4.97 × 10−20 | −2.47 | Y |
22 | 1.09 × 10−12 | 3.49 × 10−12 | 1.49 × 10−20 | 2.85 × 10−20 | −1.71 | Y |
23 | 3.76 × 10−13 | 8.72 × 10−13 | 1.84 × 10−20 | 3.05 × 10−20 | −2.36 | Y |
24 | 2.26 × 10−12 | 7.21 × 10−12 | 2.24 × 10−20 | 4.26 × 10−20 | −1.71 | Y |
25 | 6.01 × 10−16 | 1.50 × 10−15 | 3.30 × 10−22 | 6.23 × 10−22 | −2.19 | Y |
26 | 1.87 × 10−8 | 9.88 × 10−9 | 7.70 × 10−18 | 5.55 × 10−18 | −10.36 | Y |
27 | 2.11 × 10−12 | 7.50 × 10−12 | 1.53 × 10−20 | 2.38 × 10−20 | −1.54 | N |
28 | 4.11 × 10−12 | 9.48 × 10−12 | 4.93 × 10−20 | 8.81 × 10−20 | −2.37 | Y |
29 | 6.45 × 10−13 | 1.02 × 10−12 | 3.25 × 10−20 | 5.28 × 10−20 | −3.45 | Y |
30 | 2.99 × 10−13 | 5.03 × 10−13 | 2.19 × 10−20 | 4.23 × 10−20 | −3.25 | Y |
31 | 9.34 × 10−13 | 2.65 × 10−12 | 2.12 × 10−20 | 3.97 × 10−20 | −1.93 | Y |
32 | 1.71 × 10−13 | 5.44 × 10−13 | 2.56 × 10−20 | 4.14 × 10−20 | −1.72 | Y |
33 | 1.33 × 10−12 | 3.02 × 10−12 | 2.55 × 10−20 | 3.25 × 10−20 | −2.41 | Y |
34 | 5.56 × 10−20 | 2.29 × 10−19 | 4.96 × 10−24 | 2.05 × 10−24 | −1.33 | N |
35 | 4.14 × 10−13 | 8.86 × 10−13 | 1.23 × 10−19 | 3.19 × 10−19 | −2.56 | Y |
36 | 1.55 × 10−12 | 4.83 × 10−12 | 2.53 × 10−20 | 4.93 × 10−20 | −1.76 | Y |
29 |
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Carreon-Ortiz, H.; Valdez, F.; Castillo, O. Comparative Study of Type-1 and Interval Type-2 Fuzzy Logic Systems in Parameter Adaptation for the Fuzzy Discrete Mycorrhiza Optimization Algorithm. Mathematics 2023, 11, 2501. https://doi.org/10.3390/math11112501
Carreon-Ortiz H, Valdez F, Castillo O. Comparative Study of Type-1 and Interval Type-2 Fuzzy Logic Systems in Parameter Adaptation for the Fuzzy Discrete Mycorrhiza Optimization Algorithm. Mathematics. 2023; 11(11):2501. https://doi.org/10.3390/math11112501
Chicago/Turabian StyleCarreon-Ortiz, Hector, Fevrier Valdez, and Oscar Castillo. 2023. "Comparative Study of Type-1 and Interval Type-2 Fuzzy Logic Systems in Parameter Adaptation for the Fuzzy Discrete Mycorrhiza Optimization Algorithm" Mathematics 11, no. 11: 2501. https://doi.org/10.3390/math11112501