4 votes

Let A and B be two fuzzy integers defined as:

A={(1.0.3), (2, 0.6), (3, 1), (4, 0.7), (5, 0.2)}

B={(10, 0.5), (11, 1), (12, 0.5)}

Using fuzzy arithmetic operation given by

$\mu_{A+B^{(Z)}} = \underset{x+y=z}{\oplus} (\mu_A (x) \otimes \mu_B(y))$

$f(A+B)$ is _____ . [Note: $\oplus \equiv max; \: \: \otimes \equiv min$]

- {(11, 0.8), (13, 1), (15, 1)}
- {(11, 0.3), (12, 0.5), (13, 1), (14, 1), (15, 1), (16, 0.5), (17, 0.2)}
- {(11, 0.3), (12, 0.5), (13, 0.6), (14, 1), (15, 1), (16, 0.5), (17, 0.2)}
- {(11, 0.3), (12, 0.5), (13, 0.6), (14, 1), (15, 0.7), (16, 0.5), (17, 0.2)}

2 votes

A={(1,0.3), (2,0.6), (3, 1), (4, 0.7), (5, 0.2)}

B={(10, 0.5), (11, 1), (12, 0.5)}

μA+B(Z)=⊕x+y=z (μA(x)⊗μB(y)) is give as below (add elements of A and B while keeping the min membership value e.g. 1+10 =11 and min(0.3,0.5)=0.3 and so on for rest.

⊕ x + y = z {**(11,0.3)**, (12,0.3) ,(13,0.3) , **(12,0.5)**,**(13,0.6)**,(14,0.5),(13,0.5),**(14,1)**, (15,0.5),(14,0.5),**(15,0.7)**,**(16,0.5)**,(15,0.2),(16,0.2),**(17,0.2)**} by considering min membership value

now considering max membership value (in bold )

{(11,0.3) ,(12,0.5), (13,0.6), (14,1), (15,0.7), (16,0.5) ,(17,0.2)}

Hence ans is D