


'''simple docstring'''

import numpy as np
import skfuzzy as fuzz

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

     # Compute the different operations using inbuilt functions.
     a_						:       Optional[Any]      			=				np.ones(75)
     a_						:       Any      			=				np.zeros((75,))
     # 1. Union = max(µA(x), µB(x))
     a_						:       str      			=				fuzz.fuzzy_or(X, young, X, middle_aged)[1]
     # 2. Intersection = min(µA(x), µB(x))
     a_						:       Tuple      			=				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_						:       Dict      			=				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_						:       Optional[int]      			=				young + middle_aged - (young * middle_aged)
     # 6. Algebraic Product = (µA(x) * µB(x))
     a_						:       Optional[int]      			=				young * middle_aged
     # 7. Bounded Sum = min[1,(µA(x), µB(x))]
     a_						:       List[str]      			=				fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
     # 8. Bounded difference = min[0,(µA(x), µB(x))]
     a_						:       List[str]      			=				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 __snake_case      (   UpperCAmelCase_		:		int = 100	):
 lowerCamelCase_  				=						n * (n + 1) * (2 * n + 1) / 6
 lowerCamelCase_  				=						(n * (n + 1) / 2) ** 2
 return int(square_of_sum - sum_of_squares	)


if __name__ == "__main__":
     print(f'''{solution() = }''')



