UGC NET CSE | June 2014 | Part 3 | Question: 07

Question

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)

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

Comments

Option C?

Answer 1

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.

hence answer D

Answer 2

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 .