






import numpy as np
import skfuzzy as fuzz

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

     # Compute the different operations using inbuilt functions.
     lowerCamelCase__       		=  np.ones(75)
     lowerCamelCase__       		=  np.zeros((75,))
     # 1. Union = max(µA(x), µB(x))
     lowerCamelCase__       		=  fuzz.fuzzy_or(X, young, X, middle_aged)[1]
     # 2. Intersection = min(µA(x), µB(x))
     lowerCamelCase__       		=  fuzz.fuzzy_and(X, young, X, middle_aged)[1]
     # 3. Complement (A) = (1- min(µA(x))
     lowerCamelCase__       		=  fuzz.fuzzy_not(young)
     # 4. Difference (A/B) = min(µA(x),(1- µB(x)))
     lowerCamelCase__       		=  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__       		=  young + middle_aged - (young * middle_aged)
     # 6. Algebraic Product = (µA(x) * µB(x))
     lowerCamelCase__       		=  young * middle_aged
     # 7. Bounded Sum = min[1,(µA(x), µB(x))]
     lowerCamelCase__       		=  fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
     # 8. Bounded difference = min[0,(µA(x), µB(x))]
     lowerCamelCase__       		=  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 collections.abc import Callable




class       snake_case__ :

       '''simple docstring'''



       def __init__(				self      ,    a__ = None     )			->   None:






            '''simple docstring'''





            __snake_case      :list 							=    []
            # Stores indexes of each item for supporting updates and deletion.
            __snake_case      :dict 							=    {}
            # Stores current size of heap.
            __snake_case      :List[Any] 							=    0
            # Stores function used to evaluate the score of an item on which basis ordering
            # will be done.
            __snake_case      :Optional[Any] 							=    key or (lambda a__     : x)



       def        __lowercase    (				self      ,    a__     )			->   int | None:






            '''simple docstring'''





            return int((i - 1) / 2     ) if i > 0 else None



       def        __lowercase    (				self      ,    a__     )			->   int | None:






            '''simple docstring'''





            __snake_case      :int 							=    int(2 * i + 1     )
            return left if 0 < left < self.size else None



       def        __lowercase    (				self      ,    a__     )			->   int | None:






            '''simple docstring'''





            __snake_case      :Optional[int] 							=    int(2 * i + 2     )
            return right if 0 < right < self.size else None



       def        __lowercase    (				self      ,    a__      ,    a__     )			->   None:






            '''simple docstring'''





            __snake_case							,			__snake_case      :Dict 							=    (
                self.pos_map[self.arr[j][0]],
                self.pos_map[self.arr[i][0]],
            )
            # Then swap the items in the list.
            __snake_case							,			__snake_case      :Tuple 							=    self.arr[j], self.arr[i]



       def        __lowercase    (				self      ,    a__      ,    a__     )			->   bool:






            '''simple docstring'''





            return self.arr[i][1] < self.arr[j][1]



       def        __lowercase    (				self      ,    a__     )			->   int:






            '''simple docstring'''





            __snake_case      :int 							=    self._left(a__     )
            __snake_case      :Optional[int] 							=    self._right(a__     )
            __snake_case      :List[Any] 							=    i

            if left is not None and not self._cmp(a__      ,    a__     ):
                 __snake_case      :int 							=    left
            if right is not None and not self._cmp(a__      ,    a__     ):
                 __snake_case      :Tuple 							=    right

            return valid_parent



       def        __lowercase    (				self      ,    a__     )			->   None:






            '''simple docstring'''





            __snake_case      :int 							=    self._parent(a__     )
            while parent is not None and not self._cmp(a__      ,    a__     ):
                 self._swap(a__      ,    a__     )
                 __snake_case							,			__snake_case      :str 							=    parent, self._parent(a__     )



       def        __lowercase    (				self      ,    a__     )			->   None:






            '''simple docstring'''





            __snake_case      :List[Any] 							=    self._get_valid_parent(a__     )
            while valid_parent != index:
                 self._swap(a__      ,    a__     )
                 __snake_case							,			__snake_case      :Optional[int] 							=    valid_parent, self._get_valid_parent(a__     )



       def        __lowercase    (				self      ,    a__      ,    a__     )			->   None:






            '''simple docstring'''





            if item not in self.pos_map:
                 return
            __snake_case      :List[Any] 							=    self.pos_map[item]
            __snake_case      :Optional[Any] 							=    [item, self.key(a__     )]
            # Make sure heap is right in both up and down direction.
            # Ideally only one of them will make any change.
            self._heapify_up(a__     )
            self._heapify_down(a__     )



       def        __lowercase    (				self      ,    a__     )			->   None:






            '''simple docstring'''





            if item not in self.pos_map:
                 return
            __snake_case      :Dict 							=    self.pos_map[item]
            del self.pos_map[item]
            __snake_case      :Dict 							=    self.arr[self.size - 1]
            __snake_case      :List[str] 							=    index
            self.size -= 1
            # Make sure heap is right in both up and down direction. Ideally only one
            # of them will make any change- so no performance loss in calling both.
            if self.size > index:
                 self._heapify_up(a__     )
                 self._heapify_down(a__     )



       def        __lowercase    (				self      ,    a__      ,    a__     )			->   None:






            '''simple docstring'''





            __snake_case      :Optional[int] 							=    len(self.arr     )
            if arr_len == self.size:
                 self.arr.append([item, self.key(a__     )]     )
            else:
                 __snake_case      :Optional[Any] 							=    [item, self.key(a__     )]
            __snake_case      :str 							=    self.size
            self.size += 1
            self._heapify_up(self.size - 1     )



       def        __lowercase    (				self     )			->   tuple | None:






            '''simple docstring'''





            return self.arr[0] if self.size else None



       def        __lowercase    (				self     )			->   tuple | None:






            '''simple docstring'''





            __snake_case      :Optional[Any] 							=    self.get_top()
            if top_item_tuple:
                 self.delete_item(top_item_tuple[0]     )
            return top_item_tuple






def 	UpperCamelCase	(							):




     '''simple docstring'''








if __name__ == "__main__":
     import doctest

     doctest.testmod()


