A company manufacturing soft drinks is thinking of expanding its plant capacity so as to meet future demand. The monthly sale for the past 6 years are available. State, giving reasons, the type of modelling you will use to obtain good estimates for future demand so as to help the company make the right decisions. Also state four essentials and four non-essentials for the problem.

 Consider the two parents which are participating in partially mapped cross over as shown below:

Parent 1: C D | E A B |I H G F

Parent 2: A B | C D E |F G H I

Using partially mapped crossover assuming 2^nd and 6^th as the cross over sites, find the children solution.

 Computer the output for the neurons in the kohonen networks, the related data is given below:
i) Input to Kohnen neural network:
Input Neuron-1 
Input Neuron-2 
ii) Connected weights between the neurons are as given below:

 Using diagram, show the difference between feed-forward neural network and recurrent neural network.

 Consider the following table for the connections between input neurons and the hidden layer neurons:

The connection weights from the hidden layer neurons to the output neurons are -0.6, -0.3 and -0.6, for the first, second and third neurons, respectively.

Corresponding threshold value for the output layer is 0.5 and for the hidden layer is 1.8, 0.005 and 0.2 for the first, second and third neurons, respectively.
i) Draw the diagram of the network.

ii) Write the output at each node.

Determine the -cut of the fuzzy set (A) are given below, at 0.7 and 0.2.

Also, compare the -cut of the two outcomes, and give comments for status of -value variation.

 Generate the population in the next iteration by using Roulette-Wheel criterion:

 Consider a dataset of five observations given in the following table, each of which has two features f₁ and f₂:

Assume the number of cluster  and the real number . Also, assume the initial cluster centers as  and . Apply fuzzy c-mean algorithm to find the modified cluster center after one iteration.

Approximate the function  for , by solving 1-2-1 network, using Back propagation algorithm. The weighted structure and initial input are as follows:
Weighted structures are:
 and bias 
 and bias 
The initial input is 1.
Draw the architecture of the model. Perform one iteration.

 Out of three genetic operators viz. selection, cross-over and mutation, list and justify which operator or combination there of will be required for the following:

i) To fill the population with copies of the best individual from the population.
ii) For the convergence of an algorithm to good but sub-optimal solution.

Implement AND function using McCulloch-Pitts neuron.

 Let A and B be two Fuzzy sets as given below:


Determine the following:
i) Universe of discourse for Set A and Set B.
ii) Complements of Set A and Set B
iii) 
iv) 

 Consider the fuzzy sets A and B defined on the interval [0, 5]. Their membership functions are:

$

and 

Determine the membership function and graph them for each of the following:

i) A^C, B^C

ii) 

iii) 

iv) 

v) 

Find the length and order of the following schema:

i) 

ii) 

iii) 

iv) 

 Consider the ADALINE filter with three neurons in the input layer having weights 3,1 and − 2and the input sequence ......., ,0,0,0 − 0,0,0,5,4 ,.....}. Find the filter output.

 Consider the single layer perception given below:

The activation function is:

Obtain the output for each of the following input pattern:

 A single layer neural network is to have six inputs and three outputs. The outputs are continuous over the range 0 to 1. Now answer the following:
i) How many neurons are required?
ii) What are the dimensions of the weight matrix?
iii) What kind of transfer function could be used?
iv) Is a bias required? Give reasons.

Verify whether the Genetic Algorithm (GA) improves the solution from one generation to the next generation, for the function given below:
Maximize:

Subject to:

Assume that chromosomes of length 6 are created at random and modified by Roulette-Wheel selection.

Solve the network to approximate the function:

for , choosing the initial weights and bias as the random numbers.

 Determine the fuzzy relation T as a composition between the fuzzy relations R and S given below by using max-min and max-product: