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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 max-product composition is given by
a. A
b. B
c. C
d. D
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 max-min composition is given by
a. A
b. B
c. C
d. D
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)}
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
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)}
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
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
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)
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
Answer: (c).x^2 – x – 1 = 0

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

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