11.  Let R and S be two fuzzy relations defined as follows. Then, the resulting relation, T, which relates elements of universe of X to elements of universe of Z using maxproduct composition is given by 
a.  A 
b.  B 
c.  C 
d.  D 
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Answer: (d).D

12.  Let R and S be two fuzzy relations defined as follows. Then, the resulting relation, T, which relates elements of universe x to elements of universe z using maxmin composition is given by 
a.  A 
b.  B 
c.  C 
d.  D 
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Answer: (c).C

13.  Compute the value of adding the following two fuzzy integers: A = {(0.3,1), (0.6,2), (1,3), (0.7,4), (0.2,5)} B = {(0.5,11), (1,12), (0.5,13)} Where fuzzy addition is defined as μA+B(z) = maxx+y=z (min(μA(x), μB(x))) Then, f(A+B) is equal to 
a.  {(0.5,12), (0.6,13), (1,14), (0.7,15), (0.7,16), (1,17), (1,18)} 
b.  {(0.5,12), (0.6,13), (1,14), (1,15), (1,16), (1,17), (1,18)} 
c.  {(0.3,12), (0.5,13), (0.5,14), (1,15), (0.7,16), (0.5,17), (0.2,18)} 
d.  {(0.3,12), (0.5,13), (0.6,14), (1,15), (0.7,16), (0.5,17), (0.2,18)} 
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Answer: (d).{(0.3,12), (0.5,13), (0.6,14), (1,15), (0.7,16), (0.5,17), (0.2,18)}

14.  A perceptron has input weights W1 = 3.9 and W2 = 1.1 with threshold value T = 0.3. What output does it give for the input x1 = 1.3 and x2 = 2.2? 
a.  2.65 
b.  2.30 
c.  0 
d.  1 
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Answer: (c).0

15.  Let A and B be two fuzzy integers defined as: A={(1,0.3), (2,0.6), (3,1), (4,0.7), (5,0.2)} B={(10,0.5), (11,1), (12,0.5)} Using fuzzy arithmetic operation given by 
a.  {(11,0.8), (13,1), (15,1)} 
b.  {(11,0.3), (12,0.5), (13,1), (14,1), (15,1), (16,0.5), (17,0.2)} 
c.  {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,1), (16,0.5), (17,0.2)} 
d.  {(11,0.3), (12,0.5), (13,0.6), (14,1), (15,0.7), (16,0.5), (17,0.2)} 
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Answer: (d).{(11,0.3), (12,0.5), (13,0.6), (14,1), (15,0.7), (16,0.5), (17,0.2)}

16.  Let A be the set of comfortable houses given as follows. Then the set of comfortable and affordable houses is 
a.  A 
b.  B 
c.  C 
d.  D 
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Answer: (a).A

17.  Support of a fuzzy set given below, within a universal set X is given as 
a.  A 
b.  B 
c.  C 
d.  D 
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Answer: (d).D

18.  In a single perceptron, the updation rule of weight vector is given by 
a.  w(n + 1)=w(n)+η[d(n)y(n)] 
b.  w(n + 1)=w(n)–η[d(n)y(n)] 
c.  w(n + 1)=w(n)+η[d(n)y(n)]* x (n) 
d.  w(n + 1)=w(n)–η[d(n)y(n)]* x (n) 
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Answer: (c).w(n + 1)=w(n)+η[d(n)y(n)]* x (n)

19.  The golden ratio ϕ and its conjugate ϕ’ both satisfy the equation 
a.  x^3 – x – 1 = 0 
b.  x^3 + x – 1 = 0 
c.  x^2 – x – 1 = 0 
d.  x^2 + x – 1 = 0 
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Answer: (c).x^2 – x – 1 = 0

20.  At any iteration of simplex method, if Δj (Zj – Cj) corresponding to any nonbasic variable Xj is obtained as zero, the solution under the test is 
a.  Degenerate solution 
b.  Unbounded solution 
c.  Alternative solution 
d.  Optimal solution 
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Answer: (c).Alternative solution
