THEORY EXAMINATION (SEM–IV) 2016-17 INTRODUCTION TO SOFT COMPUTING (NEURAL NETWORK, FUZZY LOGIC & GENETIC ALGORITHM)

INTRODUCTION TO SOFT COMPUTING (NOE041)

SECTION – A

(Attempt All | 10 × 2 = 20 Marks)

(a) Can Artificial Intelligence be used in Neural Networks?

Yes, Artificial Intelligence (AI) can be used in neural networks. Neural networks are a core part of AI and are used to simulate human learning and decision-making processes.

(b) Applications of Neural Networks

Neural networks are used in pattern recognition, image processing, speech recognition, medical diagnosis, weather forecasting, stock market prediction, and robotics.

(c) Reinforcement Learning

Reinforcement learning is a learning method in which an agent learns by interacting with the environment and receives rewards or penalties based on its actions.

(d) Convergence of Genetic Algorithm

Convergence of a GA refers to the stage where successive generations produce very similar solutions and no significant improvement occurs in fitness values.

(e) Significance of Fuzzy Quantifier

Fuzzy quantifiers represent imprecise quantities such as “most”, “few”, or “many” and help in reasoning with vague or linguistic information.

(f) Fuzzy Inference

Fuzzy inference is the process of mapping fuzzy inputs to fuzzy outputs using a set of fuzzy rules and membership functions.

(g) Mutation

Mutation is a genetic operator that introduces random changes in chromosomes to maintain genetic diversity and avoid premature convergence.

(h) Hebb Rule for Auto-Associative Network

Given vector: [1 1 1 −1]

Weight matrix using Hebb rule:

W=XTXW = X^T XW=XTX W=[111−1][1 1 1 −1]=[111−1111−1111−1−1−1−11]W = \begin{bmatrix} 1\\1\\1\\-1 \end{bmatrix} [1\ 1\ 1\ -1] = \begin{bmatrix} 1 & 1 & 1 & -1\\ 1 & 1 & 1 & -1\\ 1 & 1 & 1 & -1\\ -1 & -1 & -1 & 1 \end{bmatrix}W=​111−1​​[1 1 1 −1]=​111−1​111−1​111−1​−1−1−11​​

Diagonal elements are set to zero.

(i) FLC

FLC stands for Fuzzy Logic Controller, used to control systems using fuzzy rules instead of mathematical models.

(j) Benefit of Genetic Algorithm

GA can solve complex optimization problems, works with large search spaces, avoids local minima, and does not require derivative information.

SECTION – B

(Attempt Any Five | 5 × 10 = 50 Marks)

(a) Artificial Neural Network & Its Characteristics

An Artificial Neural Network (ANN) is a computational model inspired by the human brain, consisting of interconnected neurons.

Characteristics:                                Learning capability

Parallel processing                            Fault tolerance

Generalization ability                        Adaptability

(b) Factors Affecting Training of Backpropagation Neural Network

Training depends on learning rate, number of hidden layers, number of neurons, initial weights, training data size, activation function, and stopping criteria.

(c) Operations on Fuzzy Sets with Examples

Common operations include union (max), intersection (min), and complement (1−μ).

Example:
If μA(x)=0.6 and μB(x)=0.4
Union = max(0.6,0.4)=0.6
Intersection = min(0.6,0.4)=0.4

(d) Selection of Parameters in Backpropagation Network

Parameters include learning rate, momentum factor, number of epochs, network architecture, and error tolerance. Proper selection improves convergence speed and accuracy.

(e) Genetic Algorithm & Flow Diagram

A Genetic Algorithm is a population-based optimization technique inspired by natural evolution.

Steps:
Initialization → Fitness Evaluation → Selection → Crossover → Mutation → New Generation → Termination

(f) Roulette Wheel Selection (Fitness vs Rank Based)

Fitness-based: Selection probability proportional to fitness value.

Rank-based: Selection probability based on rank, avoids domination by very fit individuals.

(g) Perceptron Classification Problem

Given vectors and targets, learning rate = 1, initial weights = 0.

Weights are updated using:

Wnew=Wold+η⋅t⋅xW_{new} = W_{old} + \eta \cdot t \cdot xWnew​=Wold​+η⋅t⋅x

After iterating through all patterns, final weight vector correctly classifies the given vectors.

(h) Predicate Logic Inference

Given:                                                    All men are mortal

Socrates is a man                                  Using Modus Ponens:
Therefore, Socrates is mortal.

SECTION – C

(Attempt Any Two | 2 × 15 = 30 Marks)

3) Neural Network Architectures

(i) Rosenblatt’s Perceptron Model

The perceptron is a single-layer feedforward network used for linear classification. It consists of input layer, weights, summation unit, and activation function.

Limitation: Cannot solve non-linearly separable problems.

(ii) McCulloch–Pitts Model

It is the earliest neural model using binary inputs and outputs. It performs logical operations such as AND, OR, and NOT using threshold logic units.

4) Greg Voigt’s Fuzzy Cruise Controller

A fuzzy cruise controller maintains vehicle speed using fuzzy rules instead of mathematical equations.

Inputs: Speed error, change in error
Output: Throttle position

The controller uses linguistic rules like:
“If speed is low and error is increasing, then increase throttle.”

5) Genetic Algorithm for Non-Linear Programming

Minimize:

(x−2.5)2+(y−5)2(x - 2.5)^2 + (y - 5)^2(x−2.5)2+(y−5)2

Subject to:

5.5x+2y2−18≤0,x≥0, y≥55.5x + 2y^2 - 18 \le 0,\quad x \ge 0,\ y \ge 55.5x+2y2−18≤0,x≥0, y≥5

Steps:

Encode x and y

Generate initial population

Evaluate fitness

Apply selection, crossover, mutation

Check constraints

Repeat until convergence

Optimal solution is obtained near the feasible boundary satisfying constraints.