Fuzzy Systems Multiple choice Questions and Answers-UGC NET computer science question paper

1.	Consider a fuzzy set A defined on the interval X = [0, 10] of integers by the membership Junction μA(x) = x / (x+2) Then the α cut corresponding to α = 0.5 will be
a.	{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
b.	{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
c.	{2, 3, 4, 5, 6, 7, 8, 9, 10}
d.	None of the above

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Answer: (c).{2, 3, 4, 5, 6, 7, 8, 9, 10})

2.	If A and B are two fuzzy sets with membership functions: μa(χ) ={0.2,0.5.,0.6,0.1,0.9} μb (χ)= {0.1,0.5,0.2,0.7,0.8} then the value of μa ∩ μb will be
a.	{0.2,0.5,0.6,0.7,0.9}
b.	{0.2, 0.5,0.2, 0.1,0.8}
c.	{0.1, 0.5, 0.6, 0.1,0.8}
d.	{0.1, 0.5, 0.2, 0.1,0.8}

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Answer: (d).{0.1, 0.5, 0.2, 0.1,0.8})

3.	The height h(A) of a fuzzy set A is defined as h(A) = sup A(x)
a.	h(A) = 0
b.	h(A) <0
c.	h(A)=1
d.	h(A)<1

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Answer: (c).h(A)=1)

4.	A __________ point of a fuzzy set A is a point x ∈ X at which µA(x) = 0.5
a.	Core
b.	Support
c.	Cross-over
d.	α - cut

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Answer: (c).Cross-over)

5.	Suppose the function y and a fuzzy integer number around -4 for x are given as y= (x-3)2 + 2. Around -4 = {(2, 0.3), (3, 0.6), (4, 1), (5, 0.6), (6, 0.3)} respectively. Then f (Around -4) is given by:
a.	{(2, 0.6), (3, 0.3), (6, 1), (11, 0.3)}
b.	{(2, 0.6), (3, 1), (6, 1), (11, 0.3)}
c.	{(2, 0.6), (3, 1), (6, 0.6), (11, 0.3)}
d.	{(2, 0.6), (3, 0.3), (6, 0.6), (11, 0.3)}

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Answer: (c).{(2, 0.6), (3, 1), (6, 0.6), (11, 0.3)})

6.	Given U = {1,2,3,4,5,6,7} A = {(3, 0.7), (5, 1), (6, 0.8)} then A will be: (where ~ → complement)
a.	{(4, 0.7), (2,1), (1,0.8)}
b.	{(4, 0.3.): (5, 0), (6. 0.2) }
c.	{(l, 1), (2, 1), (3, 0.3), (4, 1), (6,0.2), (7, 1)}
d.	{(3, 0.3), (6.0.2)}

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Answer: (c).{(l, 1), (2, 1), (3, 0.3), (4, 1), (6,0.2), (7, 1)})

7.	Consider a fuzzy set old as defined below Old = {(20, 0.1), (30, 0.2), (40, 0.4), (50, 0.6), (60, 0.8), (70, 1), (80, 1)} Then the alpha-cut for alpha = 0.4 for the set old will be
a.	{(40,0.4)}
b.	{50, 60, 70, 80}
c.	{(20, 0.1), (30, 0.2)}
d.	{(20, 0), (30, 0), (40, 1), (50,1), (60, 1), (70, 1), (80, 1)}

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Answer: (d).{(20, 0), (30, 0), (40, 1), (50,1), (60, 1), (70, 1), (80, 1)})

8.	Perceptron learning, Delta learning and LMS learning are learning methods which falls under the category of
a.	Error correction learning - learning with a teacher
b.	Reinforcement learning - learning with a critic
c.	Hebbian learning
d.	Competitive learning - learning without a teacher

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Answer: (a).Error correction learning - learning with a teacher)

9.	Let R and S be two fuzzy relations defined as follows. Then, the resulting relation, T, which relates elements of universe x to the elements of universe z using max-min composition is given by:
a.	(1)
b.	(2)
c.	(3)
d.	(4)

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Answer: (c).(3))

10.	What are the following sequence of steps taken in designing a fuzzy logic machine ?
a.	Fuzzification → Rule evaluation → Defuzzification
b.	Fuzzification → Defuzzification → Rule evaluation
c.	Rule evaluation → Fuzzification → Defuzzification
d.	Rule evaluation → Defuzzification → Fuzzification