For the fuzzy sets
$A = {(x_1,0.3), (x_2,0.7), (x_3,0.4)}$ and
$B = {(x_1,0.5), (x_2,0.2), (x_3,0.5)}$, the $A \cap B$ would be:
🎥 Video solution / Text Solution of this question is given below:
For fuzzy sets, the intersection operation is defined as:
$\mu_{A \cap B}(x) = \min(\mu_A(x), \mu_B(x))$
Now compute for each element:
$x_1$ : $\min(0.3, 0.5) = 0.3$
$x_2$ : $\min(0.7, 0.2) = 0.2$
$x_3$ : $\min(0.4, 0.5) = 0.4$
Thus,
$A \cap B = {(x_1,0.3),(x_2,0.2),(x_3,0.4)}$