fuzzy operations

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    """README, Author - Jigyasa Gandhi(mailto:jigsgandhi97@gmail.com)
    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().
        import matplotlib.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)
    
        plt.subplots_adjust(hspace=0.5)
        plt.show()