Two sensors based upon their detection levels and gain settings are co

Question

Two sensors based upon their detection levels and gain settings are compared. The following table of gain settings and sensor detection levels with a standard item being monitored provides typical membership values to represent the detection levels for each of the sensors.

Gain Setting	Sensor 1 detection levels	Sensor 2 detection levels
0	0	0
20	0.5	0.35
40	0.65	0.5
60	0.85	0.75
80	1	0.90
100	1	1

The universe of discourse is x = {0, 20 , 40 , 60 , 80 , 100 } . Find the membership function for the two sensors. Also, verify De-morgon’s laws for these membership functions.

07 Feb 2021

Answer :

Word Count : 297

We will solve this problem numerically in two parts: ### 1. Finding Membership Functions The given table represents discrete fuzzy membership values for Sensor 1 (\(\mu_{S1}(x)\)) and Sensor 2 (\(\mu_{S2}(x)\)). The membership functions are: \[ \mu_{S1}(x) = \begin{cases} 0, & x = 0 \\ 0.5, & x = 20 \\ 0.65, & x = 40 \\ 0.85, & x = 60 \\ 1, & x = 80 \\ 1, & x = 100 \end{cases} _____ ____ __________ _______ _______ ___ __________ _________.
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