75232-mt----advanced Neural Networks & Fuzzy Systems

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Code No: 75232/MT

M.Tech. – II Semester Regular Examinations, September, 2008 ADVANCED NEURAL NETWORKS & FUZZY SYSTEMS (Neural Networks) Time: 3hours

Max. Marks:60 Answer any FIVE questions All questions carry equal marks ---

1.a) b)

Show that, the Bivalent paradoxes as fuzzy midpoints. How do you justify that, neural and fuzzy systems are as function estimators.

2.a)

Explain the organization of brain. Also explain with schematic structure, the functions of biological neuron. Consider the logistic signal function: 1 S ( x) = , c>0 1 + e − cx i) Solve the logistic signal function S(x) for the activation x. ii) Show that x strictly increases with logistic S by showing that dx/ds>0. iii) Explain why in general the “inverse function” x increases with S if S’>0.

b)

3.a)

b) 4.a) b)

Use bipolar outer-product encoding to encode the following binary pairs (Ai, Bi) in a BAM matrix: B1 = (1 1 1 0 0 0) A1 = (1 0 1 0 1 0 1 0), A2 = (1 1 0 0 1 1 0 0), B2 = (1 0 1 0 1 0) A3 = (1 1 1 0 0 0 1 1), B3 = (1 1 0 0 1 1) Verify that the pairs (Ai, Bi) are bi-directional fixed points. Use synchronous recall. Verify that the corresponding bipolar associations (Xi, Yi) are also fixed points. Compute all Lyapunov energy values at each iteration. Explain the Additive Neural Dynamics. Explain four unsupervised learning laws. Describe different types of Hebbian learning methods and derive relevant synaptic modification relations. Contd…2

Code No: 75232/MT

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5.

With suitable diagram, derive the weight update equations for a multiplayer feed forward neural network and explain the effect of learning rate, and momentum term on weight update equations.

6.a) b)

Explain the BAM Architecture and its learning algorithm. Prove E ( A ) = E ( Ac ) = E ( A ∩ Ac ) = E ( A ∪ Ac )

c)

i be defined as: Let the two fuzzy sets i A and B i A = {( 0, 0.2 ) , (1, 0.3) , ( 2, 0.4 ) , ( 3, 0.5 )} i = {( 0, 0.5 ) , (1, 0.4 ) , ( 2, 0.3) , ( 3, 0.0 )} B i? is the following set a fuzzy relation on i A and B ( ( 0, 0 ) 0.2 ) , ( ( 0, 2 ) , 0.2 ) , ( ( 2, 0 ) , 0.2 )

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i. Give an example of a fuzzy relation on i A and B 7.a) b)

Explain the subsethood theorem. Prove the l ′ -version of the fuzzy entropy theorem: c l ′ ( A, Anear ) M ( A ∩ A ) E ( A) = = l ′ ( A, Afar ) M ( A ∪ Ac )

8.a) b)

Explain the Fuzzy Hebbs maps. Explain the Fuzzy adaptive system. *****