¿Qué es el conjunto borroso?
Borroso se refiere a algo que no está claro o es vago. Por lo tanto, Fuzzy Set es un conjunto en el que cada clave está asociada con un valor, que está entre 0 y 1 según la certeza. Este valor a menudo se denomina grado de pertenencia. El conjunto borroso se denota con un signo de tilde encima de la notación de conjunto normal.
Operaciones en conjunto borroso con código:
1. Unión:
Considere 2 conjuntos borrosos denotados por A y B, luego consideremos que Y es la unión de ellos, luego para cada miembro de A y B, Y será:
degree_of_membership(Y)= max(degree_of_membership(A), degree_of_membership(B))
EJEMPLO :
Python3
# Example to Demonstrate the
# Union of Two Fuzzy Sets
A = dict()
B = dict()
Y = dict()
A = {"a": 0.2, "b": 0.3, "c": 0.6, "d": 0.6}
B = {"a": 0.9, "b": 0.9, "c": 0.4, "d": 0.5}
print('The First Fuzzy Set is :', A)
print('The Second Fuzzy Set is :', B)
for A_key, B_key in zip(A, B):
A_value = A[A_key]
B_value = B[B_key]
if A_value > B_value:
Y[A_key] = A_value
else:
Y[B_key] = B_value
print('Fuzzy Set Union is :', Y)
Producción
The First Fuzzy Set is : {'a': 0.2, 'b': 0.3, 'c': 0.6, 'd': 0.6}
The Second Fuzzy Set is : {'a': 0.9, 'b': 0.9, 'c': 0.4, 'd': 0.5}
Fuzzy Set Union is : {'a': 0.9, 'b': 0.9, 'c': 0.6, 'd': 0.6}
2. Intersección:
Considere 2 conjuntos borrosos denotados por A y B, luego consideremos que Y es la intersección de ellos, luego para cada miembro de A y B, Y será:
degree_of_membership(Y)= min(degree_of_membership(A), degree_of_membership(B))
EJEMPLO :
Python3
# Example to Demonstrate
# Intersection of Two Fuzzy Sets
A = dict()
B = dict()
Y = dict()
A = {"a": 0.2, "b": 0.3, "c": 0.6, "d": 0.6}
B = {"a": 0.9, "b": 0.9, "c": 0.4, "d": 0.5}
print('The First Fuzzy Set is :', A)
print('The Second Fuzzy Set is :', B)
for A_key, B_key in zip(A, B):
A_value = A[A_key]
B_value = B[B_key]
if A_value < B_value:
Y[A_key] = A_value
else:
Y[B_key] = B_value
print('Fuzzy Set Intersection is :', Y)
Producción
The First Fuzzy Set is : {'a': 0.2, 'b': 0.3, 'c': 0.6, 'd': 0.6}
The Second Fuzzy Set is : {'a': 0.9, 'b': 0.9, 'c': 0.4, 'd': 0.5}
Fuzzy Set Intersection is : {'a': 0.2, 'b': 0.3, 'c': 0.4, 'd': 0.5}
3. Complemento:
Considere un conjunto borroso denotado por A, luego consideremos que Y es el complemento de este, luego para cada miembro de A, Y será:
degree_of_membership(Y)= 1 - degree_of_membership(A)
EJEMPLO :
Python3
# Example to Demonstrate the
# Difference Between Two Fuzzy Sets
A = dict()
Y = dict()
A = {"a": 0.2, "b": 0.3, "c": 0.6, "d": 0.6}
print('The Fuzzy Set is :', A)
for A_key in A:
Y[A_key]= 1-A[A_key]
print('Fuzzy Set Complement is :', Y)
Producción
The Fuzzy Set is : {'a': 0.2, 'b': 0.3, 'c': 0.6, 'd': 0.6}
Fuzzy Set Complement is : {'a': 0.8, 'b': 0.7, 'c': 0.4, 'd': 0.4}
4. Diferencia:
Considere 2 conjuntos borrosos denotados por A y B, luego consideremos que Y es la intersección de ellos, luego para cada miembro de A y B, Y será:
degree_of_membership(Y)= min(degree_of_membership(A), 1- degree_of_membership(B))
EJEMPLO :
Python3
# Example to Demonstrate the
# Difference Between Two Fuzzy Sets
A = dict()
B = dict()
Y = dict()
A = {"a": 0.2, "b": 0.3, "c": 0.6, "d": 0.6}
B = {"a": 0.9, "b": 0.9, "c": 0.4, "d": 0.5}
print('The First Fuzzy Set is :', A)
print('The Second Fuzzy Set is :', B)
for A_key, B_key in zip(A, B):
A_value = A[A_key]
B_value = B[B_key]
B_value = 1 - B_value
if A_value < B_value:
Y[A_key] = A_value
else:
Y[B_key] = B_value
print('Fuzzy Set Difference is :', Y)
Producción
The First Fuzzy Set is : {"a": 0.2, "b": 0.3, "c": 0.6, "d": 0.6}
The Second Fuzzy Set is : {"a": 0.9, "b": 0.9, "c": 0.4, "d": 0.5}
Fuzzy Set Difference is : {"a": 0.1, "b": 0.1, "c": 0.6, "d": 0.5}
Conjuntos difusos de clase
Python3
class FzSets:
def __init__(self):
self.A = dict()
self.B = dict()
self.complement_A = dict()
self.complement_B = dict()
self.union_AB = dict()
self.intersection_AB = dict()
self.differenceAB = dict()
self.differenceBA = dict()
self.change_union = False
self.change_intersection = False
self.change_complement = False
def __init__(self,A,nA,B,nB):
self.A = A
self.B = B
self.Aname = nA
self.Bname = nB
self.complement_A = dict()
self.complement_B = dict()
self.union_AB = dict()
self.intersection_AB = dict()
self.differenceAB = dict()
self.differenceBA = dict()
self.change_union = False
self.change_intersection = False
self.change_complement = False
def unionOp(self):
if self.change_union:
print('Result of UNION operation :',self.union_AB)
else:
#unionSet = set(self.A.keys()).union(self.B.keys())
sa = set(self.A.keys())
sb = set(self.B.keys())
intersectionSet = set(self.A.keys()).intersection(self.B.keys())
for i in intersectionSet:
self.union_AB[i] = max(self.A[i],self.B[i])
for i in sa-intersectionSet:
self.union_AB[i] = self.A[i]
for i in sb-intersectionSet:
self.union_AB[i] = self.B[i]
print('Result of UNION operation :',self.union_AB)
def intersectionOp(self):
if self.change_intersection:
print('Result of INTERSECTION operation :\n\t\t',self.intersection_AB)
else:
#unionSet = set(self.A.keys()).union(self.B.keys())
sa = set(self.A.keys())
sb = set(self.B.keys())
intersectionSet = set(self.A.keys()).intersection(self.B.keys())
for i in intersectionSet:
self.intersection_AB[i] = min(self.A[i],self.B[i])
for i in sa-intersectionSet:
self.intersection_AB[i] = 0.0
for i in sb-intersectionSet:
self.intersection_AB[i] = 0.0
print('Result of INTERSECTION operation :\n\t\t',self.intersection_AB)
self.change_intersection = True
def complementOp(self):
if self.change_complement:
print('Result of COMPLEMENT on ',self.Aname,' operation :',self.complement_A)
print('Result of COMPLEMENT on ',self.Bname,' operation :',self.complement_B)
else:
for i in self.A:
self.complement_A[i] = 1 - A[i]
for i in self.B:
self.complement_B[i] = 1 - B[i]
print('Result of COMPLEMENT on ',self.Aname,' operation :',self.complement_A)
print('Result of COMPLEMENT on ',self.Aname,' operation :',self.complement_B)
self.change_complement = True
def __oneMinustwo(self,L,R):
minus_d = dict()
Rcomp = dict()
for i in R:
Rcomp[i] = 1 - R[i]
sa = set(L.keys())
sb = set(R.keys())
intersectionSet = sa.intersection(sb) # min( A , complement(B) )
# l - r OR a - b
for i in intersectionSet:
minus_d[i] = min(L[i],Rcomp[i])
for i in sa-intersectionSet:
minus_d[i] = 0.0
for i in sb-intersectionSet:
minus_d[i] = 0.0
return minus_d
def AminusB(self):
self.differenceAB = self.__oneMinustwo(self.A,self.B)
print('Result of DIFFERENCE ',self.Aname,' | ',self.Bname,' operation :\n\t\t',self.differenceAB)
def BminusA(self):
self.differenceBA = self.__oneMinustwo(self.B,self.A)
print('Result of DIFFERENCE ',self.Bname,' | ',self.Aname,' operation :\n\t\t',self.differenceBA)
def change_Setz(self,A,B):
self.A = A
self.B = B
print('\nSet ',self.Aname,' :',self.A)
print('Set ',self.Bname,' :',self.B,end='')
self.change_union = True
self.change_intersection = True
self.change_complement = True
print('\t\t\t Cache Reset')
def displaySets(self):
print('\nSet ',self.Aname,' :',self.A)
print('Set ',self.Bname,' :' ,self.B)