UGC NET CSE | December 2012 | Part 3 | Question: 13

Question

Consider a fuzzy set A defined on the interval X=[0, 10]of integers by the membership Junction $\mu_A(x) = \frac{x}{x+2}$. Then the $\alpha$ cut corresponding to $\alpha =0.5 will be

• A. $\{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$
• B. $\{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$
• C. $\{ 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$
• D. $\{  \}$

Answer 1

putting value of X from 0 to 10  in membership function =x/x+2 we get

0/2 , 1/3 , 2/4 ,3/5 ,4/6 ,5/7 , 6 /8 , 7/9 , 8/10 , 9/11 , 10/12  means they are belonging with degree 0,0.33,0.5,0.6 .........0.83

here alpha cut =0.5 so first two elements will not be included in the result as their degree of belongingness  <0.5

so ans will be C   {2,3,4,5,6,7,8,9,10}