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Pre – Ph.D. EXAMINATIONS – DECEMBER 2013

Neural Networks and Fuzzy Logic

Time: 3 hours Max. Marks: 100

Answer any five of the following: 5 x 20 = 100marks

1. (a) Intelligence and Artificial Intelligence both are similar? Or dissimilar? Explain. If A->B is F and B->A is T, what is the truth value of (A->B) ^ (B->A)? Using this result and the truth table of (A->B), determine the truth table of A↔B

(b) Define the expert system with a diagram showing their components

2. (a) Prove that the minimum operator is the largest T-norm and the maximum operator is the smallest S-norm specifically, show that Min (x,y )≥ xTy and max (x,y) ≤ xSy.

Prove that xTy≤ min(x,y)≤ max(x,y)≤ XSy

3. (a) Explain about Gaussian shape function and discrete membership function?

(b) Consider a first order fuzzy dynamic system whose free (unforced; input=0) response is given by Xj+1=Xj ° R

Investigate the stability of this decision making process for the following

(i) R= 0.1 0.40.8 1.0 ii} R=

0.1 0.30.2 0.4

4. The given three layer network divides the plane with three lines forming a triangle. Calculate the weights that will give a triangle having vertices at(x,y)and coordinates (0,0),(1,3),and (3,1).

W13

W36

x w23 z w14 w46

yw15 w24

w56w25

5. Derive the back propagation training algorithm for the structure of the feed forward neural network given in which the logistic function is replaced by the hyperbolic tangent function tanh (αx) given as :

f(x)=tanh(αx) = e αx - e -αx eαx + e-αx

Notice that the derivative of f(x) is given by:

δfδx = αsech2(αx)

6. Explain with neat sketch neural network as inverse model based controller

7 Explain about hybrid neuro fuzzy system

8. The Rosenbrock Banana function is defined as follows: ƒ(xi) =100*(xi+1 - xi

2) 2 + (1-xi)2

Minimize this function over the interval [-2, 2] with an accuracy of two decimals

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