The fuzzy sets

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5.15 An outlet in a dam is regulated to maintain the level of water. Gates are opened once
water reaches more than head level. Let X be the universe of excess level of water in
feet X = {10, 20, 30, 40, 50) and Y be a universe of discharge cubic feet
Y = (5x10, 10x 104, 15× 10, 20x10, 25 x 104}. The fuzzy sets for both param-
eters are given as follows:
={17+
(0.7 0.6 0.3 0.4 0.21
10 20 + 30
+
+ +
40 50
P(x):
Pp(y) = {018-
{5010
0.6
0.4
+ 100-150% + 15x104, +20010², + 25x10², }
a. Use classical implication to find the relation IF high water level, THEN more
discharge
(0.7 0.3 0.5 0.6 0.4
+ + +
10 20 30 40 50
b. Suppose we are given a new water level as py(x) = {07 +
Transcribed Image Text:5.15 An outlet in a dam is regulated to maintain the level of water. Gates are opened once water reaches more than head level. Let X be the universe of excess level of water in feet X = {10, 20, 30, 40, 50) and Y be a universe of discharge cubic feet Y = (5x10, 10x 104, 15× 10, 20x10, 25 x 104}. The fuzzy sets for both param- eters are given as follows: ={17+ (0.7 0.6 0.3 0.4 0.21 10 20 + 30 + + + 40 50 P(x): Pp(y) = {018- {5010 0.6 0.4 + 100-150% + 15x104, +20010², + 25x10², } a. Use classical implication to find the relation IF high water level, THEN more discharge (0.7 0.3 0.5 0.6 0.4 + + + 10 20 30 40 50 b. Suppose we are given a new water level as py(x) = {07 +
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