




import numpy as np
import skfuzzy as fuzz

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

   # Compute the different operations using inbuilt functions.
   lowerCamelCase__ :   Optional[int]					=							np.ones(75)
   lowerCamelCase__ :   Optional[int]					=							np.zeros((75,))
   # 1. Union = max(µA(x), µB(x))
   lowerCamelCase__ :   Optional[Any]					=							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__ :   int					=							fuzz.fuzzy_not(young)
   # 4. Difference (A/B) = min(µA(x),(1- µB(x)))
   lowerCamelCase__ :   Optional[Any]					=							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__ :   str					=							young + middle_aged - (young * middle_aged)
   # 6. Algebraic Product = (µA(x) * µB(x))
   lowerCamelCase__ :   Union[str, Any]					=							young * middle_aged
   # 7. Bounded Sum = min[1,(µA(x), µB(x))]
   lowerCamelCase__ :   List[str]					=							fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
   # 8. Bounded difference = min[0,(µA(x), µB(x))]
   lowerCamelCase__ :   Optional[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()
from functools import lru_cache


@lru_cache
def    a__       (						__UpperCamelCase ):
      if num < 0:
            raise ValueError("Number should not be negative." )

      return 1 if num in (0, 1) else num * factorial(num - 1 )


if __name__ == "__main__":
      import doctest

      doctest.testmod()


