# Elective – I : Fuzzy Logic and Neural Networks | Nagpur University | Summer-2019

## B.E. (Electrical Engineering (Electronics & Power)) Seventh Semester (C.B.S.)Elective – I : Fuzzy Logic and Neural Networks

NRT/KS/19/3546
Time : Three Hours
Max. Marks : 80
_____________________________________________________________________
Notes : 1. All questions carry marks as indicated.
2. Solve Question 1 OR Questions No. 2.
3. Solve Question 3 OR Questions No. 4.
4. Solve Question 5 OR Questions No. 6.
5. Solve Question 7 OR Questions No. 8.
6. Solve Question 9 OR Questions No. 10.
7. Solve Question 11 OR Questions No. 12.

1. a) Given two fuzzy numbers A and B whose membership function are given by –

A (x) =  (x +2) / 2 ; for    -2  < x ≤ 0
=  (2- x )/ 2 ;   for      0 < x  < 2
=0             ; otherwise

B(x)=(x-2)/2         ;  for 2 < x < 4
= (6-x)/2       ;   for 0 < x ≤ 6
=  0               ;   otherwise

Calculate the fuzzy numbers (A+B), (A–B), (B–A), (A/B) .    [07 M]

b) Explain the standard operations performed on fuzzy set with example.  [07 M]

OR

2. a) Explain t-norms and t-conorms.   [07 M]

b) Let Z be a fuzzy set defined by $Z=\frac{0.6}{x_{1}}+\frac{0.3}{x_{2}}+\frac{0.9}{x_{3}}+\frac{0.75}{x_{4}}+\frac{1}{x_{5}}$
list all  α- cuts and strong  α cuts of Z.   [07 M]

3. a) Discuss adaptation algorithm to improve set point – control in adaptive fuzzy control.  [07 M]

b) Explain the Centre of Gravity (COG) Defuzzification method. [06 M]

OR

4. a) What are the types of FKBC, Explain any one in detail.  [07 M]

b) Enlist and explain any one application of FLC from industrial perspective.  [06 M]

5. a) Let A, B, ∈ F(x); then prove that following properties hold true for all
α,β, [0,1] ;      [07 M]

i)  (A ∩ B)αA ∩ αB
ii) $(\overline{A})_{\alpha }=(\overline{A})(1-\alpha )$

b) Explain Binary fuzzy relations.   [06 M]

OR

6. Write short notes on.   [13 M]

i) Adaptive feed forward I Feedback Fuzzy controller.   [05 M]
ii) Law of exclusive middle and absorption.   [04 M]
iii) Structure of FKBC.   [04 M]

7. a) Explain the different – steps involved in training of the neural network. What do you mean by supervised and unsupervised training process of neural networks.   [07 M]

b) Explain perception training algorithm for single mode perception neural network model.    [07 M]

OR

8. a) Explain with suitable neat diagram the “ADALINE” perception training algorithm.   [07 M]

b) Explain the Bi-directional Associative Memory (BAM) in the context of Autoassociation in first layer followed by weight matrix mapping into second layer.   [07 M]

9. a) What do you mean by feed-forward Neural Network? Explain the difference between synchronous and Asynchronous neural network.   [07 M]

b) Write a short note on Recurrent Network.   [06 M]

OR

10. a) Obtain the AND gate logic for a two I/P (External) AND – gate using single node
perception based on perceptron training algorithm. Assume initial weight as zero show the classification on atleast 3 NOS of iterations (i > = 3).  [07 M]
Assume
x0=+1
f(s)=+1;  s≥0
= -1; s<0

b) Explain recurrent associative memory storage and retrieval algorithm. [06 M]

11. Write short notes on any three.

1) Perception learning rule.   [05 M]
2) Recurrent Network.   [04 M]
3) Supervised and non supervised learning.   [04 M]
4) Counter propagation network.   [04 M]

OR

12. a) Write a short note on “Self organizing Feature Maps”.   [07 M]

b) What is ART? Explain with suitable illustration and mathematical formulation.   [06 M]

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