Assignment #1 Solution

1.    [2 marks] Write the expression for the characteristic function of the set


S


=  x |


x


>


10


.





2.    [5 marks]    Given the fuzzy set A with the membership function

A(x) =  0

for x   20


for 20 < x < 35
(x − 20)/15






for 35   x   45
1



− x)/15
for 45 < x < 60
(60







for x   60
0



    a) Sketch the graph of the function and identify its type






    b) Attach a possible linguistic description to the concept represented by fuzzy set A




    3. [3 marks] Consider fuzzy sets A and B shown in the following figure. In the same figure, sketch results of the following operations: A B, A B, NOT(A). Label resulting graphs accordingly.



A    B