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Artificial Intelligence - Fuzzy Sets

Avatto > > UGC NET COMPUTER SCIENCE > > PRACTICE QUESTIONS > > Artificial Intelligence > > Fuzzy Sets

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

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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

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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

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

 Which of the following statements is/are TRUE?
 1. A, B is a fuzzy number for any m1, m2, s1, s2
 2. A, B is a fuzzy number iff m1 ∈ [a1, a2], m2 ∈ [b1, b2]
 3. A ∩m B is a fuzzy number iff m1 ∈ [a1, a2], m2 ∈ [b1, b2] and m1 = m2
 4. A ∪m B is a fuzzy number iff m1 ∈ [a1, a2], m2 ∈ [b1, b2] and m1 = m2

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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)

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