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Artificial Intelligence - Fuzzy Sets Online Exam Quiz

Important questions about Artificial Intelligence - Fuzzy Sets. Artificial Intelligence - Fuzzy Sets MCQ questions with answers. Artificial Intelligence - Fuzzy Sets exam questions and answers for students and interviews.

1. Let R be a fuzzy relation on X × Y such that R(x, y) = 0.7 for some (x, y) ∈ X × Y. Which of the following is TRUE?

Options

A : R -1 (x, y) = 0.3

B : R -1 (x, y) = (0.7) -1

C : R -1 (y, x) = 0.7

D : R -1 (y, x) = 0.3

3. Let R be a fuzzy relation on X × Y and S be a fuzzy relation on Y × Z. Define the composition R 0 * S(x, z) = sup y {t * (R(x, y), S(y, z))}, where t * is a t-norm. Let X = Y = Z, which of the follwoing is/are correct?

Options

A : If t p is algebraic product, then R 0 p S = S 0 p R

B : If t b is algebraic product, then R 0 b S = S 0 b R

C : If t m is algebraic product, then R 0 m S = S 0 m R

D : None of the above

4. Let R = be a fuzzy relation on X × Y and R (n) = where R (n) = R 0 R (n-1) and 0 denotes max-min composition. Select the correct option(s) for n ≥ 2 1. R (n) = R 2. c = 0.5, e = 0.7 & f = 0.6 3. c = d & a = f 4. a,b,c,d,e & f depends on n

Options

A : 1, 2 and 4

B : 1, 3 and 4

C : 1, 2 and 3

D : 1, 2, 3 and 4

5. Let R be a fuzzy relation on X - {1,2,....,100} and Y-{50,51,....,100} defined by

Options

A : 1, 2 and 3

B : 2, 3 and 4

C : 1, 3 and 4

D : 1, 2, 3 and 4

46. μ C (house) = ?

Options

A : 0.90

B : 0.60

C : 0.40

D : 0.10

47. μ T (boat) = ?

Options

A : 0.60

B : 0.50

C : 0.40

D : 0.70

48. μ C|T (motorcycle) = ?

Options

A : 0.30

B : 0.40

C : 0.50

D : 0.60

49. μ C|T (car) = ?

Options

A : 0.60

B : 0.70

C : 0.5

D : 0.4

50. Let A be a fuzzy set of R, A is a fuzzy number for which of the following membership functions?

Options

A : 1 and 3

B : 5 only

C : 2 and 4

D : None of the above

51. Let A, B be fuzzy numbers, ∪ m , ∩ m denote standard fuzzy union and intersection respectively and, ∪ a , ∩ a denote algebraic sum fuzzy union and algebraic product fuzzy intersection. Which of the following is/are fuzzy numbers? 1. A , with standard complement 2. A ∩ m B 3. A ∪ m B 4. A ∪ a B 5. A ∩ a B

Options

A : 2 and 3

B : 1 and 4

C : 3, 4 and 5

D : None of the above

52. Let A = (2,4,7) and B=(4,5,6) be triangular fuzzy numbers, ∩ d , ∪ d denote drastic intersection and union respectively. Then which of the following statements is/are correct? 1. A ∩ d B is not normal 2. A ∪ d B is not normal 3. A ∩ d B is a fuzzy number 4. A ∪ d B is a fuzzy number

Options

A : 2 only

B : 1 and 3

C : 1 and 4

D : All of the above

53. Let A = (-1,2,6,8) and B = (2,4,8,10) be trapezoidal fuzzy numbers ∩ b , ∪ b denote bounded difference fuzzy intersection and bounded sum fuzzy union respectively. Then which of the following statements is/are correct> 1. A ∪ b B is a fuzzy number 2. A ∩ b B is NOT a fuzzy number 3. A ∩ m B = A ∩ b B 4. A ∪ b B ⊂ A ∪ m B

Options

A : 1, 3 and 4

B : 2, 3 and 4

C : 3 only

D : 4 only

54. Let A, B be Gaussian fuzzy sets of R such that

Options

A : 1 only

B : 1, 2 and 3

C : 2, 3 and 4

D : 4 only

55. Let A = [-1,4], B = [2,3] and C = [-5, 6]. Which of the following is/are CORRECT? 1. A.C ⊆ A.B 2. B.(A + C) ⊆ A. (B + C) 3. B.(A + C) ⊆ C. (A + B) 4. A.(B + C) ⊂ A.B + (A.C)

Options

A : 1 and 2

B : 2 and 3

C : 3 and 4

D : 1 and 4

56. Let A = [5,10], B = [1,2] and C = [-1,1]. Which of the following is/are CORRECT? 1. A - 5B = {0} 2. A = 5B 3. C.(A - 5B) = A - 5B 4. C.A - C.5B = 3(A - 5B)

Options

A : 1 and 2

B : 2 and 3

C : 3 and 4

D : 4 only

57. Let A = [-4,16], B = [2, 4]. Which of the following is/are INCORRECT? 1. A/B = [-2,4] 2. B.(A/B) = A 3. (B/B) = {1} 4. A ⊂ A.(B/B)

Options

A : 1, 2 and 3

B : 2 and 4

C : 3 and 4

D : 1 and 2

58. ∪ m , ∪ a , ∪ b and ∪ d denote fuzzy union with maximum, algebraic sum, bounded sum and drastict-conorms respectively Let A 1 , A 2 , A 3 ∈ F(X). Which of the following is/are TRUE? 1. α A 1 ∪ α A 2 ∪ α A 3 ⊆ α (A 1 ∪ m A 2 ∪ m A 3 ) 2. α A 1 ∪ α A 2 ∪ α A 3 ⊆ α (A 1 ∪ b A 2 ∪ b A 3 ) 3. α A 1 ∪ α A 2 ∪ α A 3 ⊆ α (A 1 ∪ a A 2 ∪ a A 3 ) 4. α A 1 ∪ α A 2 ∪ α A 3 ⊆ α (A 1 ∪ d A 2 ∪ d A 3 )

Options

A : 1, 2 and 3

B : 2, 3 and 4

C : 1, 3 and 4

D : 1, 2 and 4

59. ∩ m , ∩ a , ∩ b and ∩ d denote fuzzy intersection with minimum, algebraic product, bounded difference and drastic t-norms respectively Let A 1 , A 2 , A 3 ∈ F(X). Which of the following is/are TRUE? 1. α+ A 1 ∩ α+ A 2 ∩ α+ A 3 ⊇ α+ (A 1 ∩ m A 2 ∩ m A 3 ) 2. α+ A 1 ∩ α+ A 2 ∩ α+ A 3 ⊇ α+ (A 1 ∩ b A 2 ∩ b A 3 ) 3. α+ A 1 ∩ α+ A 2 ∩ α+ A 3 ⊇ α+ (A 1 ∩ a A 2 ∩ a A 3 ) 4. α+ A 1 ∩ α+ A 2 ∩ α+ A 3 ⊇ α+ (A 1 ∩ d A 2 ∩ d A 3 )

Options

A : 1, 2 and 3

B : 2, 3 and 4

C : 1, 3 and 4

D : 1, 2 and 4

60. Let A, B be fuzzy sets on R, C = α A and D = α B. Which of the following is/are Correct?

Options

A : 1 and 2

B : 1 and 3

C : 1 and 4

D : 2 and 4

61. Let A be a fuzzy set with

Options

A : 1 and 2

B : 2 and 3

C : 3 and 4

D : 2, 3 and 4

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