Ques 1.

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.

The universe of discourse is   Find the membership function for the two sensors. Also, verify De-morgon’s laws for these membership functions.

Ques 2.

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.

Ques 3.

a) Construct the α − cut at α = 4.0 for the fuzzy sets defined in Q. 1(b)

Ques 4.

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.

Ques 5.

Let A and B are two fuzzy sets and   and  then find out the following membership values: 

i)                              ii)         iii) 

iv)                              v)         vi)   

Ques 6.

Consider a dataset of six points given in the following table, each of which has two features  and  Assuming the values of the parameters c and m as 2 and the initial cluster centers  and  apply FCm algorithm to find the new cluster center after one iteration. 

	3	11
	3	10

	8	12
	10	6
	13	6
	13	5

Ques 7.

a) Define Error Correction Learning with examples.

Ques 8.

b) Write the types of Neural Memory Models. Also, give one example of each.

Ques 9.

Consider the set of pattern vectors P. Obtain the connectivity matrix (CM) for the patterns in P (four patterns). 

Ques 10.

a) Define Kohonen networks with examples.

Ques 11.

b) Describe the Function Approximation in MLP. Also, explain Generalization of MLP.

Ques 12.

a) Find the length and order of the following schema:  

i) 

ii)  

iii)  

Ques 13.

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 

Ques 14.

a) Consider the following travelling salesman problem involving 9 cities 

Determine the children solution using. 

i) Order crossover #1, assuming  and sites as the crossover sites

ii) Order crossover #2, assuming  and  as the key positions. 

Ques 15.

b) Consider the following single layer perception as shown in the following figure. 

and the activation function of each unit is defined as 

Calculate the output y of the unit for each of the following input patterns: 

Patterns
	1	0	1	1
	0	1	0	1
	0	1	1	1

Also, find the modified weights after one iteration. 

Ques 16.

Which of the following statements are true or false? Give a short proof or a counter example in support of your answers.

 a) There is chance of occurrence of the premature convergence in Roulett-wheel selection shceme used in GA.

b) Gradient based optimization methods are used when the objective function is not smooth and one needs efficient local optimization.

c) The  cut of a fuzzy set A in U is defined as A 

d) A single perception with preprocessing is neither an auto associative network nor a multiple layer neural network.

e) If W  then perception is non-linear separable.