Implementation of Fuzzy Operations on Fuzzy Sets: Code in Python, Union, Intersection, Difference, Complement Fuzzy and Proving De Morgan's Law. |

**What is Fuzzy Set?**

- A fuzzy set is an extension of the classical set.
- It has degrees of membership ranging between 0 and 1.
- It is always represented by ~ (tilde) Character.

**Fuzzy Operations:**

- Union
- Intersection
- Difference
- Complement

**Code:**

def union(A,B):

u = {}

for i in A:

if i in B:

u[i]=max(A[i],B[i])

else:

u[i]=A[i]

for i in B:

if i not in A:

u[i]=B[i]

return(u)

def intersection(A,B):

inter = {}

for i in A:

if i in B:

inter[i]=min(A[i],B[i])

else:

inter[i]=A[i]

for i in B:

if i not in A:

inter[i]=B[i]

return(inter)

def difference(A,B):

comp_b = complement(B)

diff
= intersection(A,comp_b) #A-B = A intersection B' return(diff)

def complement(A):

comp_a={}

for i in A:

comp_a[i] = round((1-A[i]),1)

return(comp_a)

def morgan(A,B):

#case 1

p = intersection(A,B)

p_bar = complement(p)

comp_a = complement(A)

#p -> A intersection B

#p_bar -> (A intersection B)bar

comp_b = complement(B)

q = union(comp_a,comp_b)

if(p_bar == q):

print(" A' u B' = ",q)

print("Thus, (A n B)' = A' u
B'")

print("Law 1 proved")

#case 2

p = union(A,B)

p_bar = complement(p)

comp_a = complement(A)

comp_b = complement(B)

q = intersection(comp_a,comp_b)

if(p_bar == q):

print("\n(A u B)' =
",p_bar)

print(" A' n B' = ",q)

print("Thus, (A u B)' = A' n
B'")

print("Law 2 proved")

print("\nHence De Morgan's Law
is proved")

#p -> A intersection B

#p_bar -> (A intersection B)bar

a=[]

n=input("Enter the elements of set A = ")

a=n.split(',')

print("Enter the membership value for each
element")

mem_a = {}

for i in a:

print(i,"= ",end='')

mem_a[i] = float(input())

print("A = ",mem_a)

b=[]

n=input("\nEnter the elements of set B = ")

b=n.split(',')

print("Enter the membership value for each
element")

mem_b = {}

for i in b:

print(i,"= ",end='')

mem_b[i] = float(input())

print("B = ",mem_b)

print("\n1.Union\n2.Intersection\n3.Difference\n4.Complement\n5.De
Morgan's Law\n6.Exit")

n=int(input("Enter your choice = "))

while(n < 6):

if(n == 1):

u = union(mem_a,mem_b)

print("Union = ",u)

elif(n == 2):

print("Intersection =
",inter)

elif(n == 3):

diff = difference(mem_a,mem_b)

print("Difference =
",diff)

elif(n == 4):

comp_a = complement(mem_a)

comp_b = complement(mem_b)

print("A's complement =
",comp_a)

print("B's complement =
",comp_b)

else:

morgan(mem_a,mem_b)

print("\n1.Union\n2.Intersection\n3.Difference\n4.Complement\n5.De
Morgan's Law\n6.Exit")

n=int(input("Enter your choice
= "))

Insert indentation wherever required!

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