Elective – I : Fuzzy Logic and Neural Networks
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]
2. a) Explain t-norms and t-conorms. [07 M]
b) Let Z be a fuzzy set defined by
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]
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)α=αA ∩ αB
b) Explain Binary fuzzy relations. [06 M]
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]
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]
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]
= -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]
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]