This document contains sample questions from modules related to fuzzy sets, neural networks, genetic algorithms, particle swarm optimization, ant colony optimization, and expert systems. The fuzzy set questions involve demonstrating DeMorgan's laws for given membership functions and constructing a fuzzy set based on membership values of income. The neural network questions involve training a Kohonen self-organizing map over two epochs and explaining the purpose of the reset mechanism in ART networks. The genetic algorithm questions involve determining non-dominating solutions for multi-objective optimization problems, describing genetic operators, and comparing single and multi-objective genetic algorithms. The remaining questions involve describing how various nature-inspired optimization techniques like particle swarm optimization and ant colony optimization

1. Sample questions from each module
I
a) Show that following fuzzy sets satisfy DeMorgans law: (3 Marks)
a. µA(x) =
1
1+5x
b. µB(x)= (
1
1+5𝑥
)
1/2
b) The membership function of a fuzzy set HIG, where HIG stands for high income group,is
defined as follows: (3 Marks)
0, if i ≤ 3
µHIG (i) =
𝑖−3
3
, if 3 ≤ i ≤ 6
1, if 6 ≤ i
The income i is given in lakh of Rupees per annum. Let U = {Joy, Jeev, Nina, Simi} be a universe of
four persons. Yearly income of Joy, Jeev, Nina, and Simi are Rs. 5 lakh, Rs. 8 lakh, Rs. 4 lakh, and
Rs. 3.5 lakh respectively. Construct a fuzzy set Rich on U where the richness of a person is given by
the membership value of his / her income with respect to the fuzzy set HIG. Compute the fuzzy
cardinality of Rich.
c) Proposition,P : If x is A then y is B (6 Marks)
Let us consider two sets of variable x and y be; X={x1,x2,x3} and Y={y1,y2},respectively
Also let us consider the following;
A = {(x1,0.5),(x2,1),(x3,0.6)}
B = {(y1,1),(y2,0.4)}
Then, given a fact expressed by the proposition x is A`, where A`={(x1,0.6),(x2,0.9),(x3,0.7)}
Derive a conclusion in the form y is B` (using generalized modus ponens(GMP)).
II
a) (8 marks)
Y1
11
X1
Y2
11
X2
X3
C1 C2

2. Suppose there are four patterns s1 = [1, 0, 0], s2 = [0, 0, 1], s3 = [1, 1, 0] and s4 = [0, 1, 1] to be
clustered into two clusters. The target Kohonen SOM, as shown in Figure, consists of three input
units and two output units. Assume Learning rate η = 0.8 and use the square of the Euclidean
distance to find the nearest cluster unit Yj.
Given Weight matrix W = [
. 5 . 3
. 8 . 5
. 4 .3
]
Compute the resultant network after two epochs of training.
b) Why reset mechanism is essential in ART networks? (4 marks)
III
a) Consider two objective functions f1 to be minimized and f2 to be maximized (8 marks)
Determine the non-dominating solutions among 1,2,3,4,5 and 6. Graphically represent the
Pareto-Optimal Front and Pareto-Optimal Ranking of these two objective functions.
b) What is the significance of crossover probability and the mutation probability during
crossover and mutation operations respectively. (4 marks)
c) Compare support vector regression and linear regression. (6 marks)
OR
IV
a) For f(x) = x2 over {0, 1 , 2, ….31} with initial x values of {13, 24, 8, 16}.
Generate the initial population; calculate fitness, select parents and show any one crossover
operation. (7 marks)
b) Write the algorithm for Roulette wheel. (7 marks)

3. Draw the Roulette wheel for six chromososmes corresponding to the table given below.
Table : Chromosomes and their fitness values
Chromosome # Fitness
1 10
2 5
3 25
4 15
5 30
6 20
c) Compare single objective and multi-objective genetic algorithms. How does a multi objective
genetic algorithm optimize the constraints? (4 marks)
V
a) Discuss how the ant colony optimization solves optimization problems. Substantiate with
suitable reasoning and equations for pheromone and distance/visibility calculations.
(8 marks)
b) When is weight and velocity updations performed during particle swarm optimization?
Substantiate with mathematical equations. (6 marks)
c) Compare Particle Swarm Optimization and Genetic algorithms to solve optimization
problems. (4 marks)
OR
VI
a) Explain the stages of development of an Expert system. (6 marks)
b) What are the main differences between hard constraints and soft constraints? Briefly
compare and contrast any two approaches to handling constraints used by Evolutionary
algorithms. (6 marks)
c) Suppose we have developed the following rules for our weather forecasting system,
(6 marks)
Rule I:If we suspect temperature is less than 20 AND there is humidity in the air Then
there are chances of rain
Rule II: If Sun is behind the clouds AND air is very cool. Then we suspect temperature is
less than 20o.
Rule III: If air is very heavy Then there is humidity in the air.
Suppose we have been given the following facts,
a) Sun is behind the clouds.
b) Air is very heavy and cool.

4. Using Forward chaining try to conclude that there are chances of rain.