Artificial Intelligence - Fuzzy Sets

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61. Let A be a fuzzy set with

Where ⌊0⌋ denotes the floor function. Which of the following is/are CORRECT?

Answer
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Option : C
Explanation :

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62. Let f be a map from X to Y. Let A_i ∈ F(x) and B_i ∈ F(Y) for i ∈ I. Which of the following is/are INCORRECT with respect to standard union and intersection?
1. f(∪_i∈IA_i) = ∪_i∈If(A_i)
2. f(∩_i∈IA_i) = ∩_i∈If(A_i)
3. f^-1(∪_i∈IB_i) = ∪_i∈If^-1(B_i)
4. f^-1(∩_i∈IB_i) = ∩_i∈If^-1(B_i)

Answer
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Option : B
Explanation :

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63. Let A be a continuous fuzzy number and f is a function on R. Under which of the following conditions we can say that ^αf(A) = f(^αA)
1. f is one-one
2. f is bijective and continuous
3. f is onto
4. f is bijective but not continuous

Answer
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Option : D
Explanation :

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64. Let f be a map from R to R. Let A be a fuzzy set on R. Which of the following statements is/are TRUE?
1. If A is a continuous (i.e. μ_A(x) is continuous) then f(A) is continuous
2. If A is a fuzzy number then f(A) is fuzzy number
3. If A is normal the f(A) is normal
4. If f(A) is normal then A is normal

Answer
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Option : C
Explanation :

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65. Let X = , Y = R, f(x) = sin(x) for x ∈ X. Let A be a fuzzy subset of X. Choose the correct options:

Answer
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Option : C
Explanation :

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