# A Fuzzy Logic example

Consider the following Question :

Given the three Linguistic variables A, B and D where each of them has three linguistic values Low,
Medium, and High. The membership functions of these variables are as follows:
A(Low)=<0,0, 10,30>, A(medium)=<10,30,30,50>, A(high)=<30,50,50,50>
B(Low)=<0.0.0.20>. B(medium)=< 0,20,20.40>, B(high)=<20,40,50,50>
D(Low)=<0,0,20,60>, D(medium)=<20,60,60,100>. D(high)=<60,100,100,100>
if these 3 variables are. related by the following 3 rules: -
RI If A is high AND B medium is Then D is high
-R2: If A is medium is OR B is low Then D is medium
R3- If B is NOT high then D is low .
Then infer the value of D for A = 20 and the B values (10, 20, 30, 40 )
Hint: Use only the given sampled values for approximations!


My Questions are as follows :

1) For rule number one we will take the minimum of value of A low and B medium ( because of AND ) and for rule number 2 we will take the maximum of values of A medium and B Low ( because if OR ) . But I don't know how to deal with Rule number 3 because of NOT ? What should I have to do here to evaluate this rule ? Edit: Could it be IF ( B is low OR B is medium ) then D Is Low instead of B is not High ?

2) For the final part do I have to evaluate the value of A ( 40) with each value of B ( 10,20,30,40) or there is an easy way to handle this values ?