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36. Let A = {(x, frac(x)); x ≥ 0}X = R, frac(x) = x - ⌊x⌋ Which of the following statements is/are correct with respect to A? 1. It is not a fuzzy set. 2. It is a fuzzy set but, not normal and not convex. 3. It is a normal fuzzy set but not convex 4. It is a normal and convex fuzzy set.
1 only
2 and 3
3 only
1 and 4
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37. Let A, B be fuzzy sets defined on a universal set X. Consider |A| + |B| = |A ∪ B| + |A ∩ B|, where |A| = Σx∈XμA(x). For which of the following does the given equality hold? 1. Standard Union and Intersection 2. Drastic Union and Intersection 3. Bounded Sum and Difference 4. Algebraic Sum and Product
1 and 2
1, 2 and 4
2, 3 and 4
1, 3 and 4
38. Which of the following is/are duals with respect to standard fuzzy complement? 1. Standard Union and Intersection 2. Drastic Union and Intersection 3. Bounded Sum and Difference 4. Algebraic Sum and Product"
1, 2 and 3
All of the above
39. Let ∩m,∩a,∩b,∩d denote fuzzy intersection with minimum, algebraic product, bounded difference and drastic t-norms respectively. Which of the following is/are TRUE? 1. α(A ∩b B) ⊆ α(A ∩m B) 2. α(A ∩d B) ⊆ α(A ∩p B) 3. α(A ∩b B) ⊆ α(A ∩p B) 4. α(A ∩p B) ⊆ α(A ∩d B)
3 and 4
40. Consider Hamacher's sum (fhs) and (fhp) Which of the following options is/are CORRECT? 1. fhs is not a fuzzy union, and hp is not a fuzzy intersection. 2. fhs is not a fuzzy union, and hp is a fuzzy intersection. 3. fhs is a fuzzy union, and hp is a fuzzy intersection but NOT dual with respect to standard complement. 4. fhs is a fuzzy union, and hp is a fuzzy intersection and dual with respect to standard complement.
4 only
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