## Soft Computing - Dec 2013

### Computer Engineering (Semester 7)

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)** Model the following as a fuzzy set using suitable membership function - ?Numbers close to 6?.(7 marks)
**1 (b)** Explain standard fuzzy membership functions.(7 marks)
**1 (c)** Determine all α - level sets and strong α-level sets for the following fuzzy set.

A= { (1, 0.2), (2, 0.5), (3, 0.8), (4, 1), (5, 0.7), (6, 0.3), }(7 marks)
**2** Design a Fuzzy Controller to determine the wash time of a domestic washing machine. Assume that the inputs are dirt and grease on the clothes. Use three descriptors for each input variable and five descriptors for output variable. Derive a set of rules for control action and defuzzification. The design should be supported by figures wherever possible. Clearly indicate that if the clothes are soiled to a larger degree the wash time required will be more.(20 marks)
**3 (a)** Determine the weights after four steps of training for Perceptron learning rule of a single neuron network starting with initial weights:-

W=[0 0]^{t}, inputs as X_{1}=[2 2]^{t},

X_{2}=[1 -2]^{t}, X_{3}=[-2, 2]^{t}, X_{4}=[-1, 1]^{t},

d_{1}=0, d_{2}=1, d_{3}=0, d_{4}=1 and c=1.(10 marks)
**3 (b)** Explain Mamdani type of Fuzzy Interface system in detail.(10 marks)
**4 (a)** Prove the following identities:-

i) For unipolar continuous activation function

f^{1}(net)=0 (1-0).

ii) For bipolar continuous activation function:-

f^{1}(net)=1/2 (1-0^{2}).(10 marks)
**4 (b)** Explain error back propagation training algorithm with the help of flowchart.(10 marks)
**5 (a)** Explain RBF network and give the comparison between RBF and MLP.(10 marks)
**5 (b)** Explain with examples linearly and non-linearly separable pattern classification.(10 marks)
**6 (a)** What is learning in neural networks? Differentiate between Supervised and Unsupervised learning.(10 marks)
**6 (b)** Explain Travelling salesperson problem using simulated Annealing.(10 marks)

### Write notes on any two of the following:

**7 (a)** Learning vector quantization.(10 marks)
**7 (b)** Derivative Free Optimization(10 marks)
**7 (c)** Winner take all learning rule,(10 marks)