Category Archives: Soft Computing

Soft Computing: answers to Qbank

Soft Computing

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Radial basis function networks

Delta learning rule (generalized delta learning rule, single layer, multi layer delta nw)

Error back propogation training algorithm

Genetic Algorithm (generate population question)

Hopfield networks

Perceptron networks (perceptron learning rule, single class, multi class perceptron nw)

Let x={a,b,c}
and y={d,e,f,g}
and R be the relation on x& y as
R is subset of cross product of x, y (x X y)
Then projection P(x)= max (R(x,y)) for all values of y
Global projection P(x,y) = max(R(x,y)) for all values of x and y
Example
R=[ 1.0 0.8 0.3 0.4
0.9 0.2 0.3 1.0
0.2 0.4 0.5 0.6]
Then
P(a)= max(1.0, 0.8, 0.3, 0.4)=1.0
P(e)=max(0.8, 0.2, 0.4)=0.8

Global projection=1.0

And cylindrical extention is cynR(x,y) = membership value of x

SC theory Question Bank

Soft Computing
  • Neural networks
    1. Explain linearly separable and non-separable pattern with examples.
    2. Explain error back propogation algorithm with the help of flowchart.
    3. Determine the weights after one iteration for Hebbian learning of a single neuron network starting with initial weight vector as W=[1 -1 0 0.5], input as x1=[1 -2 1.5 0], x2=[1 -0.5 -2 -1.5], x3=[0 1 -1 1.5] and c=1 using single bipolar binary activation function.
    4. Explain Perceptron Convergence theorem for Single layer perceptron.
    5. Radial basis function networks.
    6. Printed character recognition as an application of NN
    7. Explain Mc-Culloh Pitts Neuron model with example.
    8. A neuron with 4 inputs has the weight vector w=[1 2 3 4], the activation function is linear as f(net)=2*net. If the input vector is x=[5 6 7 8] then find the output of neuron.
    9. What is leaning rule? Compare different learning rules.
    10. A single neuron network using f(net)=sgn(net) has been train using following pairs of (Xi, Di)

X1={1 -2 3 -1} D1=-1, X2={0 -1 2 -1} D2=1, X3={-2 0 -3 -1} D3=-1

The weights obtain by perceptron learning rule are W4={3 2 6 1} where C=1

Determine the W3, W2, W1 by backtracking the training.

Determine W5, W6, W7 obtained from training further using same set of (Xi, Di)

  1. Explain with example Perceptron learning rule/ training algorithm.
  2. Explain supervised and unsupervised learning.
  3. Describe the Hopfield model.
  4. Explain architecture, storage and retrieval of pattern in BAM.
  5. For unipolar cont activation function f(net)=O(1-O) and for bipolar cont activation function f(net)=O(1-O2)/2
  • Fuzzy set theory
    1. Explain properties/ (support, core, Normality, crossover points) and alpha cut set of fuzzy set theory with examples.
    2. Draw fuzzy set using trapezoidal membership functions for “number close to 10”.
    3. Using Mamdani fuzzy model, design a fuzzy controller to determine the wash time of domestic washing machine. Assume that the inputs are dirt and grease on cloth. Use three descriptors for each input variables and five descriptors for the output variable. Derive set of rules for the control action and defuzzification. The design should be supported by figures wherever possible. Clearly state the time required for high dirt and grease on cloth.
    4. Let A={a1,a2}, B={b1,b2,b3},C={c1,c2}

Let R be relation defined on A & B as

  b1 b2 b3
a1 0.4 0.5 0
a2 0.2 0.8 0.2

Let S be relation between B & C as

  c1 c2
b1 0.2 0.7
b2 0.3 0.8
b3 1 0

Find Max-Min composition of R & S, Max-Product Composition of R & S.

  1. Explain fuzzy extension principle with example.
  2. High speed rail monitoring devices sometimes makes use of sensitive sensors to measure the deflection of the earth when the rail car passes. These deflections are measure wrt to some distance from the rail car and hence are actually very low in angle (in microradians). Let a universe of deflection be A={1 2 3 4} where A is the angle of microradians and let the universe of distance be D={1 2 5 7} where D is the distance in feet. The relation S between A & D given as
  D1 D2 D3 D4
A1 1 0.3 0.1 0
A2 0.2 1 0.3 0.1
A3 0 0.7 1 0.2
A4 0 0.1 0.4 1

Now a let a universe of rail car weights be W={1 2} where w is the weight in units of 10000 pounds. Suppose that relation between W & A is given by

  w1 W2
a1 1 0.4
a2 0.5 1
A3 0.3 0.1
A4 0 0

Then find T=Transpose of R o S using Max-min composition, using max-product composition.

  1. Design a fuzzy controller for a train leaving a station. The inputs are the distance from the station and speed of the train. The output is the amount of release of break power. Use four descriptors each using Mamdani fuzzy model.
  2. Different Fuzzy membership functions.
  3. What is defuzzification? What are the methods of defuzzification
  4. FIS using Mamdani model.
  • Hybrid Systems
    1. Draw ANFIS architecture for Sugeno fuzzy model.
    2. Explain ANFIS with neat diagram.
  • Genetic Algorithms
    1. Explain major components of GA.
    2. Explain GA with help of example.
    3. Explain different operators along with their subtypes in GA.