Discussion Forum
Que.  Consider a fuzzy set old as defined below Old = {(20, 0.1), (30, 0.2), (40, 0.4), (50, 0.6), (60, 0.8), (70, 1), (80, 1)} Then the alphacut for alpha = 0.4 for the set old will be 
a.  {(40,0.4)} 
b.  {50, 60, 70, 80} 
c.  {(20, 0.1), (30, 0.2)} 
d.  {(20, 0), (30, 0), (40, 1), (50,1), (60, 1), (70, 1), (80, 1)} 
Answer:{(20, 0), (30, 0), (40, 1), (50,1), (60, 1), (70, 1), (80, 1)} 
Fizza Mahmood :(December 19, 2020)
detail please

The alphacut of a fuzzy set is the subset of its support set for which the membership degree is greater than or equal to the given alpha value. For the fuzzy set Old = {(20, 0.1), (30, 0.2), (40, 0.4), (50, 0.6), (60, 0.8), (70, 1), (80, 1)}, the support set is {20, 30, 40, 50, 60, 70, 80}. To find the alphacut for alpha = 0.4, we need to find the subset of the support set for which the membership degree is greater than or equal to 0.4. From the given fuzzy set, we see that the membership degree for 40 is 0.4, and the membership degrees for 50, 60, 70, and 80 are all greater than 0.4. Therefore, the alphacut for alpha = 0.4 for the set Old is {40, 50, 60, 70, 80}. 
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