|
6 | 6 | Python:
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7 | 7 | - 3.5
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8 | 8 | """
|
9 |
| -# Create universe of discourse in python using linspace () |
10 | 9 | import numpy as np
|
11 |
| - |
12 |
| -X = np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False) |
13 |
| - |
14 |
| -# Create two fuzzy sets by defining any membership function (trapmf(), gbellmf(),gaussmf(), etc). |
15 | 10 | import skfuzzy as fuzz
|
16 | 11 |
|
17 |
| -abc1 = [0, 25, 50] |
18 |
| -abc2 = [25, 50, 75] |
19 |
| -young = fuzz.membership.trimf(X, abc1) |
20 |
| -middle_aged = fuzz.membership.trimf(X, abc2) |
21 |
| - |
22 |
| -# Compute the different operations using inbuilt functions. |
23 |
| -one = np.ones(75) |
24 |
| -zero = np.zeros((75,)) |
25 |
| -# 1. Union = max(µA(x), µB(x)) |
26 |
| -union = fuzz.fuzzy_or(X, young, X, middle_aged)[1] |
27 |
| -# 2. Intersection = min(µA(x), µB(x)) |
28 |
| -intersection = fuzz.fuzzy_and(X, young, X, middle_aged)[1] |
29 |
| -# 3. Complement (A) = (1- min(µA(x)) |
30 |
| -complement_a = fuzz.fuzzy_not(young) |
31 |
| -# 4. Difference (A/B) = min(µA(x),(1- µB(x))) |
32 |
| -difference = fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1] |
33 |
| -# 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))] |
34 |
| -alg_sum = young + middle_aged - (young * middle_aged) |
35 |
| -# 6. Algebraic Product = (µA(x) * µB(x)) |
36 |
| -alg_product = young * middle_aged |
37 |
| -# 7. Bounded Sum = min[1,(µA(x), µB(x))] |
38 |
| -bdd_sum = fuzz.fuzzy_and(X, one, X, young + middle_aged)[1] |
39 |
| -# 8. Bounded difference = min[0,(µA(x), µB(x))] |
40 |
| -bdd_difference = fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1] |
41 |
| - |
42 |
| -# max-min composition |
43 |
| -# max-product composition |
44 |
| - |
45 |
| - |
46 |
| -# Plot each set A, set B and each operation result using plot() and subplot(). |
47 |
| -import matplotlib.pyplot as plt |
48 |
| - |
49 |
| -plt.figure() |
50 |
| - |
51 |
| -plt.subplot(4, 3, 1) |
52 |
| -plt.plot(X, young) |
53 |
| -plt.title("Young") |
54 |
| -plt.grid(True) |
55 |
| - |
56 |
| -plt.subplot(4, 3, 2) |
57 |
| -plt.plot(X, middle_aged) |
58 |
| -plt.title("Middle aged") |
59 |
| -plt.grid(True) |
60 |
| - |
61 |
| -plt.subplot(4, 3, 3) |
62 |
| -plt.plot(X, union) |
63 |
| -plt.title("union") |
64 |
| -plt.grid(True) |
65 |
| - |
66 |
| -plt.subplot(4, 3, 4) |
67 |
| -plt.plot(X, intersection) |
68 |
| -plt.title("intersection") |
69 |
| -plt.grid(True) |
70 |
| - |
71 |
| -plt.subplot(4, 3, 5) |
72 |
| -plt.plot(X, complement_a) |
73 |
| -plt.title("complement_a") |
74 |
| -plt.grid(True) |
75 |
| - |
76 |
| -plt.subplot(4, 3, 6) |
77 |
| -plt.plot(X, difference) |
78 |
| -plt.title("difference a/b") |
79 |
| -plt.grid(True) |
80 |
| - |
81 |
| -plt.subplot(4, 3, 7) |
82 |
| -plt.plot(X, alg_sum) |
83 |
| -plt.title("alg_sum") |
84 |
| -plt.grid(True) |
85 |
| - |
86 |
| -plt.subplot(4, 3, 8) |
87 |
| -plt.plot(X, alg_product) |
88 |
| -plt.title("alg_product") |
89 |
| -plt.grid(True) |
90 |
| - |
91 |
| -plt.subplot(4, 3, 9) |
92 |
| -plt.plot(X, bdd_sum) |
93 |
| -plt.title("bdd_sum") |
94 |
| -plt.grid(True) |
95 |
| - |
96 |
| -plt.subplot(4, 3, 10) |
97 |
| -plt.plot(X, bdd_difference) |
98 |
| -plt.title("bdd_difference") |
99 |
| -plt.grid(True) |
100 |
| - |
101 |
| -plt.subplots_adjust(hspace=0.5) |
102 |
| -plt.show() |
| 12 | + |
| 13 | +if __name__ == "__main__": |
| 14 | + # Create universe of discourse in python using linspace () |
| 15 | + X = np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False) |
| 16 | + |
| 17 | + # Create two fuzzy sets by defining any membership function (trapmf(), gbellmf(),gaussmf(), etc). |
| 18 | + abc1 = [0, 25, 50] |
| 19 | + abc2 = [25, 50, 75] |
| 20 | + young = fuzz.membership.trimf(X, abc1) |
| 21 | + middle_aged = fuzz.membership.trimf(X, abc2) |
| 22 | + |
| 23 | + # Compute the different operations using inbuilt functions. |
| 24 | + one = np.ones(75) |
| 25 | + zero = np.zeros((75,)) |
| 26 | + # 1. Union = max(µA(x), µB(x)) |
| 27 | + union = fuzz.fuzzy_or(X, young, X, middle_aged)[1] |
| 28 | + # 2. Intersection = min(µA(x), µB(x)) |
| 29 | + intersection = fuzz.fuzzy_and(X, young, X, middle_aged)[1] |
| 30 | + # 3. Complement (A) = (1- min(µA(x)) |
| 31 | + complement_a = fuzz.fuzzy_not(young) |
| 32 | + # 4. Difference (A/B) = min(µA(x),(1- µB(x))) |
| 33 | + difference = fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1] |
| 34 | + # 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))] |
| 35 | + alg_sum = young + middle_aged - (young * middle_aged) |
| 36 | + # 6. Algebraic Product = (µA(x) * µB(x)) |
| 37 | + alg_product = young * middle_aged |
| 38 | + # 7. Bounded Sum = min[1,(µA(x), µB(x))] |
| 39 | + bdd_sum = fuzz.fuzzy_and(X, one, X, young + middle_aged)[1] |
| 40 | + # 8. Bounded difference = min[0,(µA(x), µB(x))] |
| 41 | + bdd_difference = fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1] |
| 42 | + |
| 43 | + # max-min composition |
| 44 | + # max-product composition |
| 45 | + |
| 46 | + # Plot each set A, set B and each operation result using plot() and subplot(). |
| 47 | + import matplotlib.pyplot as plt |
| 48 | + |
| 49 | + plt.figure() |
| 50 | + |
| 51 | + plt.subplot(4, 3, 1) |
| 52 | + plt.plot(X, young) |
| 53 | + plt.title("Young") |
| 54 | + plt.grid(True) |
| 55 | + |
| 56 | + plt.subplot(4, 3, 2) |
| 57 | + plt.plot(X, middle_aged) |
| 58 | + plt.title("Middle aged") |
| 59 | + plt.grid(True) |
| 60 | + |
| 61 | + plt.subplot(4, 3, 3) |
| 62 | + plt.plot(X, union) |
| 63 | + plt.title("union") |
| 64 | + plt.grid(True) |
| 65 | + |
| 66 | + plt.subplot(4, 3, 4) |
| 67 | + plt.plot(X, intersection) |
| 68 | + plt.title("intersection") |
| 69 | + plt.grid(True) |
| 70 | + |
| 71 | + plt.subplot(4, 3, 5) |
| 72 | + plt.plot(X, complement_a) |
| 73 | + plt.title("complement_a") |
| 74 | + plt.grid(True) |
| 75 | + |
| 76 | + plt.subplot(4, 3, 6) |
| 77 | + plt.plot(X, difference) |
| 78 | + plt.title("difference a/b") |
| 79 | + plt.grid(True) |
| 80 | + |
| 81 | + plt.subplot(4, 3, 7) |
| 82 | + plt.plot(X, alg_sum) |
| 83 | + plt.title("alg_sum") |
| 84 | + plt.grid(True) |
| 85 | + |
| 86 | + plt.subplot(4, 3, 8) |
| 87 | + plt.plot(X, alg_product) |
| 88 | + plt.title("alg_product") |
| 89 | + plt.grid(True) |
| 90 | + |
| 91 | + plt.subplot(4, 3, 9) |
| 92 | + plt.plot(X, bdd_sum) |
| 93 | + plt.title("bdd_sum") |
| 94 | + plt.grid(True) |
| 95 | + |
| 96 | + plt.subplot(4, 3, 10) |
| 97 | + plt.plot(X, bdd_difference) |
| 98 | + plt.title("bdd_difference") |
| 99 | + plt.grid(True) |
| 100 | + |
| 101 | + plt.subplots_adjust(hspace=0.5) |
| 102 | + plt.show() |
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