
import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
     # Create universe of discourse in Python using linspace ()
     lowerCamelCase__    :		Any          =   np.linspace(start=0, stop=7_5, num=7_5, endpoint=True, retstep=False)

     # Create two fuzzy sets by defining any membership function
     # (trapmf(), gbellmf(), gaussmf(), etc).
     lowerCamelCase__    :		int          =   [0, 2_5, 5_0]
     lowerCamelCase__    :		List[str]          =   [2_5, 5_0, 7_5]
     lowerCamelCase__    :		List[Any]          =   fuzz.membership.trimf(X, abca)
     lowerCamelCase__    :		List[str]          =   fuzz.membership.trimf(X, abca)

     # Compute the different operations using inbuilt functions.
     lowerCamelCase__    :		List[Any]          =   np.ones(7_5)
     lowerCamelCase__    :		List[Any]          =   np.zeros((7_5,))
     # 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__    :		Dict          =   fuzz.fuzzy_and(X, young, X, middle_aged)[1]
     # 3. Complement (A) = (1- min(µA(x))
     lowerCamelCase__    :		Optional[Any]          =   fuzz.fuzzy_not(young)
     # 4. Difference (A/B) = min(µA(x),(1- µB(x)))
     lowerCamelCase__    :		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__    :		Dict          =   young + middle_aged - (young * middle_aged)
     # 6. Algebraic Product = (µA(x) * µB(x))
     lowerCamelCase__    :		int          =   young * middle_aged
     # 7. Bounded Sum = min[1,(µA(x), µB(x))]
     lowerCamelCase__    :		Tuple          =   fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
     # 8. Bounded difference = min[0,(µA(x), µB(x))]
     lowerCamelCase__    :		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, 1_0)
     plt.plot(X, bdd_difference)
     plt.title("""bdd_difference""")
     plt.grid(True)

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






from __future__ import annotations

from collections.abc import Iterator
from typing import Any



class       _snake_case   :


 def __init__(					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   lowercase__  :   Any    		=      data
   lowercase__  :   Node | None    		=      None



class       _snake_case   :


 def __init__(					self):


   '''simple docstring'''




   lowercase__  :   List[Any]    		=      None
   lowercase__  :   int    		=      None


 def __iter__(					self):


   '''simple docstring'''




   lowercase__  :   List[str]    		=      self.head
   while self.head:
     yield node.data
     lowercase__  :   str    		=      node.next
     if node == self.head:
       break


 def __len__(					self):


   '''simple docstring'''




   return sum(1 for _ in self)


 def __repr__(					self):


   '''simple docstring'''




   return "->".join(str(SCREAMING_SNAKE_CASE_) for item in iter(self))


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   self.insert_nth(len(self)					,  SCREAMING_SNAKE_CASE_)


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   self.insert_nth(0					,  SCREAMING_SNAKE_CASE_)


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_					,  SCREAMING_SNAKE_CASE_):


   '''simple docstring'''




   if index < 0 or index > len(self):
     raise IndexError("""list index out of range.""")
   lowercase__  :   Optional[int]    		=      Node(SCREAMING_SNAKE_CASE_)
   if self.head is None:
     lowercase__  :   Union[str, Any]    		=      new_node  # first node points itself
     lowercase__  :   Dict    		=      new_node
   elif index == 0:  # insert at head
     lowercase__  :   int    		=      self.head
     lowercase__  :   int    		=      new_node
   else:
     lowercase__  :   List[str]    		=      self.head
     for _ in range(index - 1):
       lowercase__  :   Union[str, Any]    		=      temp.next
     lowercase__  :   int    		=      temp.next
     lowercase__  :   Optional[Any]    		=      new_node
     if index == len(self) - 1:  # insert at tail
       lowercase__  :   Union[str, Any]    		=      new_node


 def      lowercase__     (					self):


   '''simple docstring'''




   return self.delete_nth(0)


 def      lowercase__     (					self):


   '''simple docstring'''




   return self.delete_nth(len(self) - 1)


 def      lowercase__     (					self					,  SCREAMING_SNAKE_CASE_ = 0):


   '''simple docstring'''




   if not 0 <= index < len(self):
     raise IndexError("""list index out of range.""")
   lowercase__  :   str    		=      self.head
   if self.head == self.tail:  # just one node
     lowercase__  :   List[Any]    		=      None
   elif index == 0:  # delete head node
     lowercase__  :   str    		=      self.tail.next.next
     lowercase__  :   List[Any]    		=      self.head.next
   else:
     lowercase__  :   Optional[int]    		=      self.head
     for _ in range(index - 1):
       lowercase__  :   List[Any]    		=      temp.next
     lowercase__  :   Optional[Any]    		=      temp.next
     lowercase__  :   Dict    		=      temp.next.next
     if index == len(self) - 1:  # delete at tail
       lowercase__  :   Tuple    		=      temp
   return delete_node.data



 def      lowercase__     (					self):


   '''simple docstring'''




   return len(self) == 0

def 		UpperCamelCase	(      )		->	None:


  '''simple docstring'''






  lowercase__  :   int    		=      CircularLinkedList()
  assert len(lowercase_   ) == 0
  assert circular_linked_list.is_empty() is True
  assert str(lowercase_   ) == ""

  try:
    circular_linked_list.delete_front()
    raise AssertionError  # This should not happen
  except IndexError:
    assert True  # This should happen

  try:
    circular_linked_list.delete_tail()
    raise AssertionError  # This should not happen
  except IndexError:
    assert True  # This should happen

  try:
    circular_linked_list.delete_nth(-1   )
    raise AssertionError
  except IndexError:
    assert True

  try:
    circular_linked_list.delete_nth(0   )
    raise AssertionError
  except IndexError:
    assert True

  assert circular_linked_list.is_empty() is True
  for i in range(5   ):
    assert len(lowercase_   ) == i
    circular_linked_list.insert_nth(lowercase_ , i + 1   )
  assert str(lowercase_   ) == "->".join(str(lowercase_   ) for i in range(1 , 6   )   )

  circular_linked_list.insert_tail(6   )
  assert str(lowercase_   ) == "->".join(str(lowercase_   ) for i in range(1 , 7   )   )
  circular_linked_list.insert_head(0   )
  assert str(lowercase_   ) == "->".join(str(lowercase_   ) for i in range(0 , 7   )   )

  assert circular_linked_list.delete_front() == 0
  assert circular_linked_list.delete_tail() == 6
  assert str(lowercase_   ) == "->".join(str(lowercase_   ) for i in range(1 , 6   )   )
  assert circular_linked_list.delete_nth(2   ) == 3

  circular_linked_list.insert_nth(2 , 3   )
  assert str(lowercase_   ) == "->".join(str(lowercase_   ) for i in range(1 , 6   )   )

  assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
     import doctest

     doctest.testmod()






