## Neural Networks and Fuzzy Systems - Dec 2014

### Electronics Engineering (Semester 8)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1 (a)** What do you mean by learning and list different learning rule.(5 marks)
**1 (b)** Explain Hebbian learning rule.(5 marks)
**1 (c)** Explain Fuzzification and defuzzitication process.(5 marks)
**1 (d)** What are the salient features of Kohonen's self organizing learning algorithm.(5 marks)
**2 (a)** What are the learning strategies in RBF(10 marks)
**2 (b)** Explain perceptron learning rule convergence theorem(10 marks)
**3 (a)** Explain different fuzzy membership function.(10 marks)
**3 (b)** What are the learning factors of back propagation algorithm.(10 marks)
**4 (a)** What is the Hopfield model of neural network ? Explain its algorithm and differentiate discrete and continuous Hopfield model in terms of energy
landscape and stable state.(10 marks)
**4 (b)** i) Compare RBF and MLP

(ii) How do you achieve fast learning in ART 2 network.(10 marks)
**5 (a)** Perform two training steps of the network using delta learning rule of λ=1 and c=0.25. Train the network using following data pairs.

$$\left ( x_{1}=\begin{bmatrix}
2\\0
\\-1
\end{bmatrix}d_{1}=-1 \ltbr\gt Use f(net)=1/0(1-0\ltsup\gt2\lt/sup\gt)
\right ), \left ( x_{2} -\begin{bmatrix}
1\\-2
\\-1
\end{bmatrix},d_{2}-1\right )$$ The initial weight are w^{1}=[101]^{t}(10 marks)
**5 (b)** Find max-min composition and max-product composition.

$$R=\begin{bmatrix}
0.8 &0.1 &0.1 &0.7 \\0
&0.8 &0 &0 \\0.9
&1 &0.7 &0.8
\end{bmatrix} S=\begin{bmatrix}
0.4 &0.9 &0.3 \\0
&0.4 &0 \\0.9
&0.5 &0.8 \\0.6
&0.7 &0.5 \end{bmatrix}$$(10 marks)
**6 (a)** Explain Back prorogation algorithm.(10 marks)
**6 (b)** If a fuzzy set defined by:

$$A=\frac{0.5}{x_{1}}+\frac{0.4}{x_{2}}+\frac{0.7}{x_{3}}+\frac{1}{x_{4}} $$List all α cuts of set A(10 marks)

### Write short note on (any four)

**7 (a)** Boltzman machine(5 marks)
**7 (b)** LMS algorithm(5 marks)
**7 (c)** Brain state in box model(5 marks)
**7 (d)** Crossover and mutation(5 marks)
**7 (e)** Bias and threshold in context of artificial neural network(5 marks)
**7 (f)** Method steepest descent(5 marks)
**7 (g)** Fuzzy controller(5 marks)