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

Course: B.Tech (All Branches – Common Elective)
Subject Code: EOE041
Subject Title: Introduction to Soft Computing (Neural Network, Fuzzy Logic & Genetic Algorithm)
Exam Type: Theory
Duration: 3 Hours
Maximum Marks: 100

SECTION – A (10 × 2 = 20 Marks)

Short and conceptual questions from Neural Networks, Fuzzy Systems, and Genetic Algorithms.

SECTION – B (5 × 10 = 50 Marks)

Descriptive and numerical questions testing in-depth conceptual understanding.

Key Topics:

(a) Artificial Neural Network (ANN):

Defined as a massively parallel system of interconnected neurons capable of learning from data.

Characteristics: Learning ability, adaptivity, non-linearity, fault tolerance, generalization.

(b) Backpropagation Neural Network (BPN):

A supervised learning algorithm minimizing mean square error via gradient descent.

Training factors: Learning rate, momentum, number of hidden layers, initialization weights, and activation functions.

(c) Fuzzy Set Operations:

Union: μA∪B(x)=max[μA(x),μB(x)]μ_{A∪B}(x) = max[μ_A(x), μ_B(x)]μA∪B​(x)=max[μA​(x),μB​(x)]

Intersection: μA∩B(x)=min[μA(x),μB(x)]μ_{A∩B}(x) = min[μ_A(x), μ_B(x)]μA∩B​(x)=min[μA​(x),μB​(x)]

Complement: μ¬A(x)=1−μA(x)μ_{¬A}(x) = 1 - μ_A(x)μ¬A​(x)=1−μA​(x)

Example: Let μA(x)=0.6,μB(x)=0.8μ_A(x)=0.6, μ_B(x)=0.8μA​(x)=0.6,μB​(x)=0.8 ⇒ A∪B=0.8,A∩B=0.6A∪B=0.8, A∩B=0.6A∪B=0.8,A∩B=0.6.

(d) BPN Parameter Selection:

Learning rate controls speed of convergence.

Momentum reduces oscillation.

More hidden neurons increase accuracy but may cause overfitting.

(e) Genetic Algorithm (GA):

A stochastic optimization algorithm inspired by natural selection.

Flowchart:
 Initialize population
 Evaluate fitness
 Selection
 Crossover
 Mutation
 Termination condition

(f) Roulette Wheel Selection (Fitness vs Random Based):

Fitness-based: Probability ∝ fitness value.

Random-based: Probability uniformly distributed.

Example: Higher fitness → larger “wheel segment”.

(g) Perceptron Classification:
Given:

Class 1 → (1,1,1,1), (-1,1,-1,-1)

Class -1 → (1,1,1,-1), (1,-1,-1,1)

Learning rate (η) = 1, initial weights = 0

Apply perceptron learning rule:

• wnew=wold+η(t−y)xw_{new} = w_{old} + η(t - y)xwnew​=wold​+η(t−y)x

to calculate final weights for classification.

(h) Predicate Logic Inference Example:
Statements:

All men are mortal.

Socrates is a man.

Therefore, Socrates is mortal.
→ Proven using modus ponens in first-order logic.

SECTION – C (2 × 15 = 30 Marks)

Analytical and applied questions from all three domains.

Q3. Neural Network Architectures

(i) Rosenblatt’s Perceptron:

Linear classifier; single-layer network.

Learning rule updates weights to minimize classification error.

(ii) McCulloch–Pitts Model:

Simplest neuron model using threshold logic.

Performs basic logical operations like AND, OR, NOT.

Q4. Fuzzy Logic Application – Greg Viot’s Fuzzy Cruise Controller

Used in automobiles for automatic speed regulation.

Components:

Fuzzification: Converts inputs (speed, acceleration) to fuzzy sets.

Inference Engine: Applies fuzzy rules (e.g., “If speed < desired then accelerate”).

Defuzzification: Converts fuzzy output to crisp control action.

Q5. Genetic Algorithm for Optimization

Problem:

Minimize (x−2.5)2+(y−5)2\text{Minimize } (x - 2.5)^2 + (y - 5)^2 Minimize (x−2.5)2+(y−5)2

Subject to:

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

Steps:
 Encode x,yx, yx,y as binary strings.
 Evaluate fitness f(x,y)f(x,y)f(x,y).
 Apply selection, crossover, and mutation.
 Use constraints as penalty terms in fitness evaluation.
 Continue until population converges to optimal (x=2.5,y=5)(x=2.5, y=5)(x=2.5,y=5).

Summary

This EOE041 – Introduction to Soft Computing exam assesses understanding of hybrid intelligent systems combining: