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66. Let X = {0,1,2,...,5}, Y = {0,1,2,...64} and f(x) = x3 be a map from X to Y. Let be a fuzzy subset of Y and A = f-1(B). Which of the following is/are INCORRECT? 1. μA(5) = 0 2. μA(4) = 0.7 3. μA(5) < 0 4. μA(1) < 0.3
1, 2 and 3
2, 3 and 4
1, 3 and 4
3 and 4
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67. Let A, B be fuzzy subsets of Z and f: Z x Z → Z given by f(x,y) = ex+y. if and C = f(A, B). Which of the following is/are CORRECT? Note that for binary functions μC(z) = Sup{(x,y)|f(x,y) = z}{min(μA(x), μB(x))} 1. |c| = 5.7 2. μC(ei) < μC(ej) for i ∈ {0,1,2} and j ∈ {4,5,6} 3. μC(e2) = 1 4. μC(1) = 1/2
1 and 2
2 and 3
2 and 4
68. Let A, B be continuous fuzzy numbers. Then which of the following is/are CORRECT? 1. 0+(A) ⊆ 0+(A + B) 2. 1(A.B) ⊆ 1A ∩ 1B 3. 1MIN(A,B) ⊆ 1A ∪ 1B 4. MIN(A,B) and MAX(A,B) are continuous fuzzy numbers
1 and 4
69. Let A, B be fuzzy numbers, C = MIN(A, B) and D = MAX(A,B). Then which of the following is/are CORRECT? 1. μC(z) = sup{min(μA(x), μB(y))|x+y = z} 2. μC(z) = sup{min(μA(x), μB(y))|min(x,y) = z} 3. μC(z) = sup{min(μA(x), μB(y))|max(x,y) = z} 4. μC(z) = sup{max(μA(x), μB(y))|x+y = z}
1 only
2 only
70. Let A = [0 1 2], B = [1 2 3] and C = A.B. Using extension principle μC(z) = sup{a1,a2,...,anz}, where ai's are μA(x) or μB(y), x and y depends on z. Then which of the following is/are CORRECT? 1. n0 = ∞, n1=n3 = 3 2. nz = ∞ 3. n4 = n5 = n6 = 2 4. n4 = n5 = 2
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be a fuzzy subset of Y and A = f-1(B). Which of the following is/are INCORRECT?
1. μA(5) = 0
2. μA(4) = 0.7
3. μA(5) < 0
4. μA(1) < 0.3
