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11. Which one of the following statements is TRUE?
Law of contradiction is followed by both Crisp and Fuzzy sets.
Law of contradiction is followed by neither Crisp set not Fuzzy set.
Law of Contradiction is followed by Fuzzy set but not Crisp set.
Law of contradiction is followed by Crisp set but not Fuzzy set.
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12. Fig. A shows triangular membership function distribution of a Fuzzy set. The value of membership (μ) corresponding to x = 8.0 is found to be equal to
0.7
0.6
0.8
0.5
13. The membership function distribution of a fuzzy set is assumed to follow a Gaussian distribution with mean m = 200 and standard deviation σ = 50. Its 0.7-cut is approximately found to be as follows:
(110.8567, 289.1433)
(157.7699, 242.2300)
(150.0000, 250.0000)
(120.3356, 279.6644)
14. Let us consider a fuzzy set A(x) = {(x1, 0.3), ((x2, 0.4), (x3, 0.5), (x4, 0.6)}. Its complement A(x) is determined as follows:
{(x1, 0.6), ((x2, 0.5), (x3, 0.4), (x4, 0.3)}
{(x1, 0.4), ((x2, 0.3), (x3, 0.6), (x4, 0.5)}
{(x1, 0.7), ((x2, 0.6), (x3, 0.5), (x4, 0.4)}
{(x1, 0.1), ((x2, 0.2), (x3, 0.3), (x4, 0.4)}
15. Let us consider two fuzzy sets: A(x) = {(x1, 0.2), ((x2, 0.3), (x3, 0.4), (x4, 0.5)} A(x) = {(x1, 0.3), ((x2, 0.4), (x3, 0.5), (x4, 0.6)}. Their intersection (A ∩ B)(x) is determined as
{(x1, 0.3), ((x2, 0.4), (x3, 0.5), (x4, 0.6)}
{(x1, 0.2), ((x2, 0.3), (x3, 0.4), (x4, 0.5)}
{(x1, 0.5), ((x2, 0.3), (x3, 0.1), (x4, 0.2)}
{(x1, 0.3), ((x2, 0.2), (x3, 0.4), (x4, 0.5)}
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