We want to compare two motion sensors based upon their signal levels and moving settings. For a universe of discourse of moving settings, M= {0, 20, 40, 60, 80, 100), the actuator signal levels for the controlling of a standard item provides typical membership functions to represent the signal levels for each of the motion sensors; these are given below in standard discrete form: (0 0.5 0.65 0.85 1.0, 1.0) S₁ + + 20 40 80 +100 + 60 (ii) (iii) 5₂ = 1+ 0.45 0.6 0.8 0.95 1.0) + + + + 20 40 60 80 100 Solve the following membership functions using standard fuzzy operations: μS₁ U S₂(x) μ S₁ S₂(x) μl S₁ (x)

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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(a)
We want to compare two motion sensors based upon their signal levels and moving
settings. For a universe of discourse of moving settings, M = {0, 20, 40, 60, 80, 100),
the actuator signal levels for the controlling of a standard item provides typical
membership functions to represent the signal levels for each of the motion sensors;
these are given below in standard discrete form:
(0 0.5 0.65 0.85 1.0
+
+ +
20 40 60 80
(i)
(ii)
(iii)
(iv)
5₁ = { +
$₂
=
μ 5₁ (x)
μ S₂ (x)
1.0)
100)
Solve the following membership functions using standard fuzzy operations:
μ S₁ U S₂(x)
μS₁ S₂(x)
0.45 0.6 0.8 0.95 1.0)
+ + +
+
20 40 60 80 100)
Transcribed Image Text:(a) We want to compare two motion sensors based upon their signal levels and moving settings. For a universe of discourse of moving settings, M = {0, 20, 40, 60, 80, 100), the actuator signal levels for the controlling of a standard item provides typical membership functions to represent the signal levels for each of the motion sensors; these are given below in standard discrete form: (0 0.5 0.65 0.85 1.0 + + + 20 40 60 80 (i) (ii) (iii) (iv) 5₁ = { + $₂ = μ 5₁ (x) μ S₂ (x) 1.0) 100) Solve the following membership functions using standard fuzzy operations: μ S₁ U S₂(x) μS₁ S₂(x) 0.45 0.6 0.8 0.95 1.0) + + + + 20 40 60 80 100)
8
(vi)
μ S₁ U S₂(x)
μS, n 5₂(x)
Transcribed Image Text:8 (vi) μ S₁ U S₂(x) μS, n 5₂(x)
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