

import numpy as np
import skfuzzy as fuzz

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

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





			"""simple docstring"""







			snake_case:    Optional[int]      							=len(__UpperCAmelCase					)
			snake_case:    Optional[int]      							=[[0] * n for i in range(__UpperCAmelCase					)]
			for i in range(__UpperCAmelCase					):
						snake_case:    Optional[int]      							=y_points[i]

			for i in range(2				,							__UpperCAmelCase					):
						for j in range(__UpperCAmelCase				,							__UpperCAmelCase					):
									snake_case:    List[str]      							=(
									    (xa - x_points[j - i + 1]) * q[j][i - 1]
									    - (xa - x_points[j]) * q[j - 1][i - 1]
									) / (x_points[j] - x_points[j - i + 1])

			return [q[n - 1][n - 1], q]


if __name__ == "__main__":
	import doctest

	doctest.testmod()




