Today I Learned

Some of the things I've learned every day since Oct 10, 2016

113: One Generalization of AND, OR, NOT to Fuzzy Logic

In fuzzy logic, where the set \{ 0, 1 \} of possible values is replaced with the range [ 0, 1], generalizations of the basic AND, OR, and NOT operators is needed which can handle input from the new domain. The only requirement of such generalizations is that they agree with their more specific counterparts when given input from \{ 0, 1 \}. However, there are choices which are more intuitive and advantageous than others.

One such choice is defining

  • AND(a, b) = a*b
  • OR(a, b) = a + b – a*b
  • NOT(a) = 1 – a

The formulas for AND and NOT are intuitive enough, and even though the formula for OR may not be, it’s easily derived from those of the other 2 using the equivalence

OR(a, b) = NOT(AND(NOT(a), NOT(b))).



Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: