SFIT,Mumbai
G.Anuradha
BE: COMPUTERS
Soft Computing
Date: 14/09/2012
Time: 10:00-12:00
Max marks: 75
___________________________________________
Note the following instructions.
1. Attempt all 5 questions.
2. Draw neat diagrams wherever necessary.
3. Choose the best or the most appropriate answer(s) in case of multiple choice
questions. Give proper explanation to support your answer.
4. All sub-questions of the same question should be answered at one place only in
their serial order, and not scattered.
5. Write everything in ink (no pencil) only.
6. All sub questions are to be answered together
1a Define extension principle and explain with an example
A is a fuzzy set on X :
A   A ( x1 ) / x1   A ( x2 ) / x2     A ( xn ) / xn
The image of A under f() is a fuzzy set B:
B   B ( x1 ) / y1   B ( x2 ) / y2     B ( xn ) / yn
where yi = f(xi), i = 1 to n, µA(xi )=µB(xi).
If f() is a many-to-one mapping, then
 B ( y)  max  A ( x)
x  f 1 ( y )
Suppose that function f is a mapping from an n-dimensional Cartesian product space X1 
X2  …  Xn to a 1-dimensional universe Y s.t. y=f(x1, …, xn), and suppose A1, …, An are n
(5)
SFIT,Mumbai
G.Anuradha
fuzzy sets in X1, …, Xn, respectively.
Then, the extension principle asserts that the fuzzy set B induced by the mapping f is
defined by
1b What are the features of membership function? Explain core, support, boundaries, normality,
crossover points with a neat diagram
(5)
2a Given A={a1 a2} B={b1 b2 b3} C={c1 c2}. R is a relation from A to B and S is a relation from (5)
B to C given by
R=0.4 0.5 0
S= 0.2 0.7
0.2 0.8 0.2
0.3 0.8
1.0 0
Find RoS using max-min
RoS=max(min(.4,.2),min(.5,.3),min(0,1))=0.3
Max(min(.4,.7),(.5,.8),(0,0))=0.5
Max(min(.2,.2),min(.0.8,.3),(.2,1))=0.3
Max(min(.2,.7),(.8,.8),(.2,0))=0.8
Answer 0.3 0.5
0.3 0.8
SFIT,Mumbai
G.Anuradha
2b Explain Sugeno Fuzzy Inference Systems?
(5)
3
(10)
Design a fuzzy controller for controlling the temperature of water from a shower which is
controlled by an angular shaft. Use 3 linguistic variables for input and 3 linguistic variables for
output and form the rule base. Prove that extreme left position of shaft gives you very cold water
from the shower.
1. for proper inputs -2 marks
2. for proper outputs-2 marks
3. for input output membership values 2 marks
4. for rule base-2 marks
5. proof-2 marks
SFIT,Mumbai
G.Anuradha
4a Draw and explain the block diagram of EBPTA
(10)
4b Determine the weights after 1 iteration for hebbian learning of a single neuron network starting
with initial weights w=[-1 1], inputs as X1=[1 -2] ;X2=[2 3]; X3 = [1 -1] and learning constant
c=1; use Unipolar continuous activation fn.
X1 X2 net
F(net)
W1
W2
Delta
Delta w2
-1
1
w1
1
-2 -3
0.0474 -0.9526 0.9052 0.0474
-0.0948
(10)
2
3
0.8104
0.6922
0.4318
1.3844
2.0766
0.0724
-0.0724
2.9818
1
-1
2.5500
0.0724
2.9094
0.5042
SFIT,Mumbai
G.Anuradha
5a Explain RBF network and show how EXOR problem can be solved using RBF
(10)
5b Write the algorithm of Learning Vector Quantization
(8)
SFIT,Mumbai
5c What is Elitism? What are the components of GA?
Encoding schemes
Fitness evaluation
Selection
Crossover
Mutation
G.Anuradha
(7)