Fuzzy Logic Simplified: Understanding the Basics

[pikapika!]

Can someone please give an idiots definition of fuzzy logic?

 

[phoenixthoth]

Idiot's definition, eh? C'mon, you're not an idiot!

Here goes...

There is logic and then there is fuzzy logic. Logic might also be called Aristotlean logic, standard logic, or crisp logic. Crisp to contrast with fuzzy.

Elementary logic has to do with defining formulas, which are composed of terms, and then assigning truth values to those formulas depending on the truth values of the terms.

A tautology is a formula that is true regardless of the truth value of its terms. An example is (A ^ (A->B))->B, where the connective ^ is "and". That is an example of a formula and a tautology.

In logic, there are TWO truth values. The truth value set, if you want to call it that, is {T,F} or {true, false}.

In fuzzy logic, there are MORE THAN TWO truth values. AFAIK, the truth set is [0,1], the set of real numbers not less than 0 and not greater than 1. There, 0 corresponds to F and 1 corresponds to T.

In ternary logic, there are three truth values. The truth set is {0,1/2,1}.

If you google "fuzzy logic application" you'll get an idea what it is "good for."

(Note that in ternary logic, under few assumptions, modus ponens is NOT a tautology.)

 

[ramollari]

Fuzzy logic is actually a substitution of excessively complex mathematical models when reasoning about vague concepts that are true to a degree.

 

[HallsofIvy]

Essentially, every proposition is assigned a probability that it is true. That's what phoenixthoth was saying. I'm not at all sure what ramollari was saying!

 

[matt grime]

How about this translation of ramollari's post:

fuzzy logic is an attempt by engineers to do probability theory without realizing someone already beat them to it.

Not that I've anything against the subject you understand... (actually that's an approximate quote from someone who used to work with AI people has said to me).

 

[ramollari]

Halls of ivy, what I said was straightforward. It is MUCH easier to reason with vague concepts (i.e. fuzzy variables) like High, Low, Many, Few, Fast, Big, etc. with the rules of fuzzy logic, rather than reason with actual numbers that are combined with complex devised mathematical models.

By the way, the value assigned to variables [0,1] are not probabilities (reasoning under uncertain conditions), but degrees of truth (reasoning under vague conditions).

 

[gnome]

Please distinguish between your interpretations of "uncertain" and "vague".

 

[ramollari]

'Uncertain' is used when we don't know the outcome of an event, so it involves probability. For example, if someone has flu he may have fever with a probability of 0.8. We cannot just write if someone has flu then he has fever, because it involves uncertainty.
'Vague' is used when we have all data (outcomes), but the meaning of language is vague. For example, we know the speed of a car, but we don't know to what degree it is Fast, because the language meaning of Fast is vague.

 

[Icebreaker]

fuzzy logic is an attempt by engineers to do probablity theory without realizing someone already beat them to it.

Is this a joke, or is fuzzy logic really a redundant form of probability?

 

[matt grime]

It's a joke dismissing the abilities of engineers to do mathematics as also being a joke. It isn't my joke. But the papers I've read on things such as "reasoning in the absence of full information" tend to make me think the author is taking the piss too.

 

[TenaliRaman]

Fuzzy logic decreases complexity of calculations whereas applying bayes (which is used usually in predictive rule-inference mechanisms) takes up lot of computation time. Thats basically the reason why engineers stick to "fuzzy" logic instead of "perfect" probability.

Althought i believe the joke was not to mean any harm still the idea of using fuzzy logic is that its a trade off between speed and accuracy.

-- AI

 

[chroot]

The central tenent of fuzzy logic is the division of "truth" into a number of categories.

A standard thermostat controlling a heater, for example, recognizes only two categories: the temperature is greater than the setpoint, or the temperature is lower than the setpoint.

A fuzzy-logic thermostat has more sense to it: it recognizes temperatures that are much, much too low, temperatures that are too low, but don't represent an emergency, temperatures that are lower than they should be, temperatures that are about right, and so on. This thermostat can make more efficient use of energy by making more intelligent decisions about when to turn the heater on, how long to leave it on, and so on.

- Warren

 

[TenaliRaman]

Also one more point to note is that, all those stuff that we can do using fuzzy logic can be done using probability as well.

-- AI

 

[ramollari]

How? Please expand.

 

[TenaliRaman]

See if this helps
http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail96/0642.html

If something is still unclear then let me know.
For those who read the link:
Note that the post i am pointing to refers to the "usability" of fuzzy logic and not its relationship with probability. The post should probably highlight some of the points as to why fuzzy logic outperforms probability in many cases but still it cannot be denied that its roots can be found in probability. So don't write a post saying that it says probability and fuzzy logic are not same , i never claimed they are same! (Kapeesh!) (Just being on the safe side, after a long experience from a debate with a person on this very same subject :P)

-- AI

 

[cronxeh]

Is fuzzy logic linear or nonlinear?