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Que. Consider a fuzzy set A defined on the interval X = [0, 10] of integers by the membership Junction
 μA(x) = x / (x+2)
Then the α cut corresponding to α = 0.5 will be
a. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
b. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
c. {2, 3, 4, 5, 6, 7, 8, 9, 10}
d. None of the above
Answer:{2, 3, 4, 5, 6, 7, 8, 9, 10}
Milind :(February 10, 2020) I want to know the solution's explanation
...
To find the α-cut of a fuzzy set A, we need to determine the values of x in the universe of discourse X for which the membership function μA(x) is greater than or equal to α. In this case, we have:

μA(x) = x / (x+2) ≥ 0.5

Multiplying both sides by (x+2), we get:

x ≥ 0.5x + 1

Subtracting 0.5x from both sides, we get:

0.5x ≥ 1

Dividing both sides by 0.5, we get:

x ≥ 2

Therefore, the α-cut of A for α = 0.5 is [2, 10].
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Samathmika :(December 15, 2020) Starting from 0, substitute the values in the membership function. U will find that at 2 the membership function will result in 0.5 . Hence the answer is 2 to 10.
Hope it helps !!
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Khan :(August 10, 2021) Consider a fuzzy set A defined on the interval X = [0, 10] of integers by the membership Junction
μA(x) = x / (x+2)
Then the α cut corresponding to α = 0.4will be
To find the α-cut of a fuzzy set A, we need to determine the values of x in the universe of discourse X for which the membership function μA(x) is greater than or equal to α. In this case, we have:

μA(x) = x / (x+2) ≥ 0.4

Multiplying both sides by (x+2), we get:

x ≥ 0.4x + 0.8

Subtracting 0.4x from both sides, we get:

0.6x ≥ 0.8

Dividing both sides by 0.6, we get:

x ≥ 4/3

Therefore, the α-cut of A for α = 0.4 is [4/3, 10].
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