a) Two sensors based upon their detection levels and gain settings are compared. The following of gain setting 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 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 Find the membership function for the two sensors. Also, verify De-morgon’s laws for these membership functions.
### Step 1: Define the Membership Functions The given table provides detection levels for two sensors at different gain settings. We can define the membership functions \( \mu_1(x) \) and \( \mu_2(x) \) for Sensor 1 and Sensor 2, respectively. #### Membership Functions For Sensor 1: \[ \mu_1(x) = \begin{cases} 0 & x = 0 \\ 0.5 & x _________ _____ ______ _____ ___.
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b) Consider a subset of natural numbers from 1 to 30, as the universe of discourse, U. Define the fuzzy sets “small” and “medium” by enumeration.
b) Apply the “very” hedge on the fuzzy sets defined in Q. 1(b) to get the new modified fuzzy sets. Show the modified fuzzy sets through numeration.
a) Define Kohonen networks with examples.
Let A and B are two fuzzy sets and and
then find out the following membership values:
i) ii)
iii)
iv) v)
vi)
a) Two sensors based upon their detection levels and gain settings are compared. The following of gain setting 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 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 Find the membership function for the two sensors. Also, verify De-morgon’s laws for these membership functions.
b) Let an activation function be defined as
Show that What is the value of
at the origin? Also, find the value of
as v approaches
and
b) Describe the Function Approximation in MLP. Also, explain Generalization of MLP.