#### Fuzzy Operations

```"""
Requirements:
- scikit-fuzzy
- numpy
- matplotlib
Python:
- 3.5
"""
import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
# Create universe of discourse in Python using linspace ()
X = np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False)

# Create two fuzzy sets by defining any membership function
# (trapmf(), gbellmf(), gaussmf(), etc).
abc1 = [0, 25, 50]
abc2 = [25, 50, 75]
young = fuzz.membership.trimf(X, abc1)
middle_aged = fuzz.membership.trimf(X, abc2)

# Compute the different operations using inbuilt functions.
one = np.ones(75)
zero = np.zeros((75,))
# 1. Union = max(µA(x), µB(x))
union = fuzz.fuzzy_or(X, young, X, middle_aged)[1]
# 2. Intersection = min(µA(x), µB(x))
intersection = fuzz.fuzzy_and(X, young, X, middle_aged)[1]
# 3. Complement (A) = (1- min(µA(x))
complement_a = fuzz.fuzzy_not(young)
# 4. Difference (A/B) = min(µA(x),(1- µB(x)))
difference = fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
# 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
alg_sum = young + middle_aged - (young * middle_aged)
# 6. Algebraic Product = (µA(x) * µB(x))
alg_product = young * middle_aged
# 7. Bounded Sum = min[1,(µA(x), µB(x))]
bdd_sum = fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
# 8. Bounded difference = min[0,(µA(x), µB(x))]
bdd_difference = fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1]

# max-min composition
# max-product composition

# Plot each set A, set B and each operation result using plot() and subplot().
from matplotlib import pyplot as plt

plt.figure()

plt.subplot(4, 3, 1)
plt.plot(X, young)
plt.title("Young")
plt.grid(True)

plt.subplot(4, 3, 2)
plt.plot(X, middle_aged)
plt.title("Middle aged")
plt.grid(True)

plt.subplot(4, 3, 3)
plt.plot(X, union)
plt.title("union")
plt.grid(True)

plt.subplot(4, 3, 4)
plt.plot(X, intersection)
plt.title("intersection")
plt.grid(True)

plt.subplot(4, 3, 5)
plt.plot(X, complement_a)
plt.title("complement_a")
plt.grid(True)

plt.subplot(4, 3, 6)
plt.plot(X, difference)
plt.title("difference a/b")
plt.grid(True)

plt.subplot(4, 3, 7)
plt.plot(X, alg_sum)
plt.title("alg_sum")
plt.grid(True)

plt.subplot(4, 3, 8)
plt.plot(X, alg_product)
plt.title("alg_product")
plt.grid(True)

plt.subplot(4, 3, 9)
plt.plot(X, bdd_sum)
plt.title("bdd_sum")
plt.grid(True)

plt.subplot(4, 3, 10)
plt.plot(X, bdd_difference)
plt.title("bdd_difference")
plt.grid(True)