Discussion Forum
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

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To find the αcut 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 αcut 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 αcut 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 αcut of A for α = 0.4 is [4/3, 10]. 
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