1.3k views

Given

$U=\{1, 2, 3, 4, 5, 6, 7 \} \\ A =\{(3, 0.7), (5, 1), (6, 0.8) \}$

then $\tilde{A}$ will be: (where $\sim \rightarrow$ complement)

1. $\{(4, 0.7), (2, 1), (1, 0.8)\}$
2. $\{(4, 0.3), (5, 0), (6, 0.2)\}$
3. $\{(1, 1), (2, 1), (3, 0.3), (4, 1), (6, 0.2), (7, 1) \}$
4. $\{(3, 0.3), (6, 0.2)\}$

recategorized | 1.3k views
+1
Option C?

+1 vote

for finding Compliment the value of U is taken one by one and value of set A is subtracted from (u,1) pair element wise. and the resultant is written in answer. for (5,1) it results in (0,0) so not placed in the resultant set.

by Active (1.9k points)
Complement of a fuzzy set

The complement of a fuzzy set A is a new fuzzy set A Complement, containing all the elements which are in the universe of discourse but not in A, with the membership function

Complement of µA(x) = 1 - µA(x)

So, the complement of A will be

{(1,1),(2,1),(3,0.3),(4,1),(6,0.2),(7,1)}

The first is (1,1). The first 1 is in U but not in A, so it should be added in the complement. The second 1 is because the membership function is 1- µA(x). 1-0=1.

The same reason why you get (2,1).

The third one (3,0.3) because it is (3,1-0.7)=(3,0.3).

Same reason why you have (4,1) and (7,1).

(6,1-0.8)=(6,0.2).

The member (5,0) is not included because , a singleton whose membership to a fuzzy set is 0, can be excluded .
by Boss (13.7k points)

+1 vote