تالار گفتمان مانشت

دوستان میشه یه کمک فوری بکنید جواب بدید

Exercises
I. Model the following expressions as fuzzy sets:
a. Large integers
b. Very small numbers
c. Medium-sized men
d. Numbers approximately between 10 and 20
e. High speeds for racing cars
FUZZY SETS-BASIC DEFINITIONS 21
2. Determine all a-level sets and all strong a-level sets for the following fuzzy
sets:
a. A = {(3, 1), (4, .2), (5, .3), (6, .4), (7, .6), (8, .8), (10, 1), (12, .8),
(14, .6))
b. jj = {(x, llii(X) = (1 + (x - 10)2rl)}
for a = .3, .5, .8
c. C = {(x, Ile(x)) I x ER}
where Ilc(x) = 0 for x ::5 10
Ilc(x) = (1 + (x - 1Or2r 1 for x> 10
3. Which of the fuzzy sets of exercise 2 are convex and which are not?
4. Lex X = { 1, 2, ... , 10}. Determine the cardinalities and relative cardinalities
of the following fuzzy sets:
a. A from exercise 2a
b. jj = { (2, .4), (3, .6), (4, .8), (5, 1), (6, .8), (7, .6), (8, .4) }
c. C = { (2, .4), (4, .8), (5, 1), (7, .6) }
5. Determine the intersections and unions of the following fuzzy sets:
a. The fuzzy sets A, jj, and C from exercise 4
b. jj and C from exercise 2
6. Determine the intersection and the union of the complements of fuzzy sets
jj and C from exercise 4.