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UGC NET CSE | June 2014 | Part 3 | Question: 08

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Consider a fuzzy set old as defined below

Old =$ \left\{(20, 0.1), (30, 0.2), (40, 0.4), (50, 0.6), (60, 0.8), (70, 1), (80, 1)\right\}$.

Then the alpha-cut for alpha = $0.4$ for the set old will be 

  1. $\left\{(40, 0.4)\right\}$ 
  2. $\left\{50, 60, 70, 80\right\}$
  3. $\left\{(20, 0.1), (30, 0.2)\right\}$ 
  4. $\left\{(20, 0), (30, 0), (40, 1), (50, 1), (60, 1), (70, 1), (80, 1)\right\}$ 
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alpha cut means it is the cut off value . the number having member ship value more than or equal to  in the given fuzzy set will be considered as present  in the result . now in the set OLD person with age 40,50,60,70,80 are having membership values more than or equal to 0.4 so they are considered as member with value 1    and 20 30 with value less than cut off are not member hence they are shown with value 0 so

ans is D ( P.S. it is one form of showing the result another may be {40,50,60,70,80} but it is not in choice )
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In the fuzzy set old the alpha value is compared with value of set and if it is greater than or equal to alpha value it is replaced by 1 otherwise by zero.

 

Hence answer is D

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