Model the following expressions as fuzzy sets: Large integers Very small numbers
ID: 914250 • Letter: M
Question
Model the following expressions as fuzzy sets: Large integers Very small numbers Medium-sized men Numbers approximately between 10 and 20 High speeds for racing cars Determine all a-level sets and all strong a-level sets for the following fuzzy sets: A bar = {(3, 1), (4, .2). (5, .3), (6, .4), (7, .6), (8, .8), (10, 1), (12, .8), (14, .6)} B bar = {(x, Mu_b(x)) = (1 + (x - 10)^2)^-1)} for alpha = .3, .5, .8 C bar = {(x, Mu_C (x))|x element R} where Mu_c(x) = 0 for x 10 Which of the fuzzy sets of exercise 2 are convex and which are not Let X = {1, 2.....10}. Determine the cardinalities and relative cardinalities of the following fuzzy sets: A bar from exercise 2a B bar = {(2, .4), (3, .6), (4, .8), (5, 1), (6, .8), (7, .6), (8, .4)} C={(2, .4), (4, .8), (5. 1). (7. .6)) Determine the intersections and unions of the following fuzzy sets: The fuzzy sets A bar, B bar, and C bar from exercise 4 B bar and C bar from exercise 2 Determine the intersection and the union of the complements of fuzzy sets B bar and C bar from exercise 4.Explanation / Answer
Let us assume x as concentration of TCA.
We are required to convert gal to litre and feet to metre
200 gal = 757 L
1.5 x 106 gal = 5678117.6 L
10ft = 1 Metre
Rate of mass in lake =x * 200 gal/min
Loss of TCA through Volatilization = 3 x 10-4 µg/cm2.s * {5678117.6/1000 m3}/1
= 1.7034 µg/s
Loss due to biodegradation = biodegradation rate x loss of TCA by Volatilization
= 6X10-3 * 1.7034 µg/s = 0.0075 µg/s
Outlet flow rate of TCA =1.5*106/200 =7500 gal = 28390 Litre
From conservation law
Rate of mass in = rate of mass out+ loss due to volatilization + loss due to biodegradation
5678117 * x = 28390 + 1.7034 + 0.0075 = 28391.71
x= 28391.71/5678117 = 0.005000 µg/l = 5 ppb
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