Fuzzy Logic brief introduction

Fuzzy Logic

In the traditional computer logic, the truth value could be 0 or 1, so if we ask a question to computer :

" Is it cold today? " the answer will only "Yes" or "No". It cannot understand " a little cold" or " very

cold ", but Fuzzy logic can handle the concept of truth with many value between completely true and

completely false, it helps AI to take an important step.

As the below plot, the temperature is separated by dichotomy logic, cold or not called crisp set.

 But human's feeling often contain ambiguous narratives in semantics, in order to express more

accurately, the dichotomy extend to many-valued logic.

An fuzzy set called "membership function", it is a set of numbers which mapping between truth and

psychological. For example,  the following are 4 commonly used membership functions:

We can understand the relationship easily between the temperature and the degree of each word.

Fuzzy Inference

rules:

IF ___ IS ___ , THEN ___ IS ___ .

ex:

IF _temperature_ IS _ cold_ , THEN _fan speed_ IS _slow_ .

IF _temperature_ IS _ hot_ , THEN _fan speed_ IS _high_ .

Zadeh operators

NOT x = (1 - truth(x))

x AND y = minimum(truth(x), truth(y))

x OR y = maximum(truth(x), truth(y))

Fuzzy Logic vs Probability

Fuzzy logic is using pretty much the same tools as probability theory. But it's using them to trying to

capture a very different idea. Fuzzy logic is all about degrees of truth - about fuzziness and partial or

relative truths. Probability theory is interested in trying to make predictions about events from a state

of partial knowledge. But probability theory says nothing about how to reason about things that aren't

entirely true or false.