





import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
  # Create universe of discourse in Python using linspace ()
  __lowerCAmelCase							:     List[str]		     =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).
  __lowerCAmelCase							:     Tuple		     =[0, 25, 50]
  __lowerCAmelCase							:     Any		     =[25, 50, 75]
  __lowerCAmelCase							:     List[Any]		     =fuzz.membership.trimf(X, abca)
  __lowerCAmelCase							:     Optional[Any]		     =fuzz.membership.trimf(X, abca)

  # Compute the different operations using inbuilt functions.
  __lowerCAmelCase							:     Tuple		     =np.ones(75)
  __lowerCAmelCase							:     Dict		     =np.zeros((75,))
  # 1. Union = max(µA(x), µB(x))
  __lowerCAmelCase							:     List[str]		     =fuzz.fuzzy_or(X, young, X, middle_aged)[1]
  # 2. Intersection = min(µA(x), µB(x))
  __lowerCAmelCase							:     List[str]		     =fuzz.fuzzy_and(X, young, X, middle_aged)[1]
  # 3. Complement (A) = (1- min(µA(x))
  __lowerCAmelCase							:     Union[str, Any]		     =fuzz.fuzzy_not(young)
  # 4. Difference (A/B) = min(µA(x),(1- µB(x)))
  __lowerCAmelCase							:     Tuple		     =fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
  # 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
  __lowerCAmelCase							:     int		     =young + middle_aged - (young * middle_aged)
  # 6. Algebraic Product = (µA(x) * µB(x))
  __lowerCAmelCase							:     List[Any]		     =young * middle_aged
  # 7. Bounded Sum = min[1,(µA(x), µB(x))]
  __lowerCAmelCase							:     str		     =fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
  # 8. Bounded difference = min[0,(µA(x), µB(x))]
  __lowerCAmelCase							:     Union[str, Any]		     =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)

  plt.subplots_adjust(hspace=0.5)
  plt.show()










'''simple docstring'''

def 						UpperCamelCase    (							_lowerCamelCase : int	):

    if not isinstance(_lowerCamelCase						,	_lowerCamelCase	):
        A__    =      F"Input value of [number={number}] must be an integer"
        raise TypeError(_lowerCamelCase	)

    if number < 1:
        A__    =      F"Input value of [number={number}] must be > 0"
        raise ValueError(_lowerCamelCase	)

    A__    =      1

    for i in range(1						,	_lowerCamelCase	):
        current_number *= 4 * i - 2
        current_number //= i + 1

    return current_number


if __name__ == "__main__":
  import doctest

  doctest.testmod()



