THEORY EXAMINATION (SEM–VI) 2016-17 NEURAL NETWORKS AND FUZZY SYSTEM

NEURAL NETWORKS AND FUZZY SYSTEM

Section-wise Solved Answers & Notes (NEE013)

SECTION – A (10 × 2 = 20 Marks)

Short & precise answers

(a) Use of bias weight in artificial neuron

Bias shifts the activation function left or right. It helps a neuron fire even when inputs are zero and improves learning flexibility.

(b) Structural organization of biological neural system

Stimulus → Receptors → Sensory Neurons → Brain (Processing) → Motor Neurons → Effectors

(c) Hebbian Learning Rule

Hebbian rule states:

If two neurons are activated simultaneously, the connection weight between them increases.
Mathematically:
Δw = ηxy

(d) Auto-associative vs Hetero-associative Memory

(e) Relation between Neural Networks & Machine Learning

Neural networks are a subset of machine learning used for pattern recognition, prediction, and classification through learning from data.

(f) Fuzzy Intersection & Bounded Difference

Given:
A = {(2,1), (4,0.3), (6,0.5), (8,0.2)}                      B = {(2,0.5), (4,0.4), (6,0.1), (8,1)}

Fuzzy Intersection (min):
{(2,0.5), (4,0.3), (6,0.1), (8,0.2)}

Bounded Difference (A − B):
max(0, μA − μB)                                               {(2,0.5), (4,0), (6,0.4), (8,0)}

(g) Delta Rule vs Gradient Descent

(h) ANN vs Conventional Computing

(i) Learning & its types

Learning is adjustment of weights based on experience.

• Supervised: Target output given                        • Unsupervised: No target output

(j) Crisp relation vs Fuzzy logic

Crisp logic has true/false (0 or 1), while fuzzy logic allows degrees of truth (0 to 1).

SECTION – B (Any 5 × 10 = 50 Marks)

Answer outlines (write in detail in exam)

(a) Back Propagation Algorithm                          • Initialize weights randomly
• Forward pass → compute output                      • Calculate error
• Backward pass → update weights                     • Adjust learning rate
• Repeat till error is minimum

Error correction uses gradient descent to minimize error.

(b) Hebbian Learning & AND Gate

Hebbian learning strengthens weights when input and output are same.
For bipolar AND gate:
Weights chosen so neuron fires only when both inputs are +1.

(c) Multilayer Feed Forward Network

• Input layer → Hidden layer(s) → Output layer           • No feedback loops
• Used in classification
Difference from recurrent networks: Recurrent networks have feedback and memory.

(d) Defuzzification

Converts fuzzy output to crisp value.

• Centroid Method: Center of area                              • Weighted Average: Weighted mean
• Center of Largest Area: Midpoint of largest membership

(e) Fuzzy Inference System (FIS)

Steps:                                                                               Fuzzification

Rule evaluation                                                               Aggregation

Defuzzification                                                                Used in control systems.

(f) Linguistic Variables & Relation R                                Fabrics → Dirt → Detergent used
Example:
Cotton + Very dirty → High detergent                            Silk + Less dirty → Low detergent

(g) Learning Techniques in NN

• Supervised                                                                   • Unsupervised
• Reinforcement

Momentum factor speeds convergence and avoids local minima.

(h) Activation Functions

• Step                                                                              • Sigmoid
• Tanh                                                                              • ReLU

They decide neuron output and non-linearity.

SECTION – C (Any 2 × 15 = 30 Marks)

Q3 Short Notes (Any three)

(i) Linear Separability                                 Perceptron works only when data is linearly separable.

(ii) LR-Type Fuzzy Numbers                       Defined by left and right membership functions.

(iii) Max-Min Composition                         Used to combine fuzzy relations.

(iv) Rosenblatt’s Perceptron                       Single-layer classifier with adjustable weights.

(v) Fuzzy Entropy Theorem                        Measures fuzziness/uncertainty in fuzzy sets.

Q4 Fuzzy Set Operations

• Union (max)                                             • Intersection (min)
• Complement (1 − μ)

Explain properties: commutativity, associativity, idempotency.

Q5 Fuzzy Back Propagation System           • Combines fuzzy logic + neural learning
• Learning adjusts membership functions  • Inference uses fuzzy rules
 

Used in intelligent control systems.