CBSE NET JUNE 2012 PAPER III

If two fuzzy sets A and B are given with membership functions μA(x) = {0.2, 0.4, 0.8, 0.5, 0.1} μB(x) = {0.1, 0.3, 0.6, 0.3, 0.2} Then the value of μ – will be A∩B

(A) {0.9, 0.7, 0.4, 0.8, 0.9}

(B) {0.2, 0.4, 0.8, 0.5, 0.2}

(C) {0.1, 0.3, 0.6, 0.3, 0.1}

(D) {0.7, 0.3, 0.4, 0.2, 0.7}

(A) {0.9, 0.7, 0.4, 0.8, 0.9}

(B) {0.2, 0.4, 0.8, 0.5, 0.2}

(C) {0.1, 0.3, 0.6, 0.3, 0.1}

(D) {0.7, 0.3, 0.4, 0.2, 0.7}

Ans: (A)

Explanation:-

The fuzzy intersection of two fuzzy sets A and B on universe of discourse,

The fuzzy intersection of two fuzzy sets A and B on universe of discourse,

X: μA∩B(x) = min [μA(x), μB(x)] , where x∈X

But here in the question, they are asking for complement of A∩B and so the answer would be 1-min[A(x),B(x)]. The minimum of 0.2 and 0.1 will be 0.1, and 1-0.1 will be 0.9.

The second value is min(0.4,0.3)=0.3 and 1-0.3=0.7But here in the question, they are asking for complement of A∩B and so the answer would be 1-min[A(x),B(x)]. The minimum of 0.2 and 0.1 will be 0.1, and 1-0.1 will be 0.9.

The third value is min(0.8,0.6)=0.6 and 1-0.6=0.4

The fourth value is min(0.5,0.3)=0.3 and 1-0.3=0.7

The fifth value is min(0.1,0.2)=0.1 and 1-0.1=0.9

So the option is (A) which having { 0.9,0.7,0.4,0.7,0.9}. Its ok if fourth value is 0.8 instead of 0.8.