Discussion
If \(\underset{\sim}{A}\) = near 0.74 = \(\{ \frac{0}{0.730} + \frac{0.8}{0.735} + \frac{1}{0.740}\) \(+ \frac{0.6}{0.745} + \frac{0}{0.750} \}\)
and \(\underset{\sim}{B}\) = in 0.74 = \(\{ \frac{0}{0.730} + \frac{0.4}{0.735} + \frac{0.8}{0.740}\) \(+ \frac{1}{0.745} + \frac{0.6}{0.750} \}\)
then \(\overline{A \cup B}\) is :
Answer: D
The complement of the union is option D: grades 1, 0.2, 0, 0, 0.4 at 0.730, 0.735, 0.740, 0.745 and 0.750.
For fuzzy sets, the union takes the maximum grade at each point and the complement takes 1 minus the grade.
| x | A | B | max | 1 - max |
|---|---|---|---|---|
| 0.730 | 0 | 0 | 0 | 1 |
| 0.735 | 0.8 | 0.4 | 0.8 | 0.2 |
| 0.740 | 1 | 0.8 | 1 | 0 |
| 0.745 | 0.6 | 1 | 1 | 0 |
| 0.750 | 0 | 0.6 | 0.6 | 0.4 |
Option A has 0.4 and 1 in the last two places, the complement of A alone; option B uses the complement of the intersection in places; and option C has a grade of 2, which is impossible for a fuzzy set.
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