# What is fuzzy logic?

1. Jan 9, 2005

### pikapika!

Can someone please give an idiots definition of fuzzy logic?

2. Jan 9, 2005

### 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.)

3. Feb 17, 2005

### ramollari

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

4. Feb 17, 2005

### 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!

5. Feb 17, 2005

### matt grime

fuzzy logic is an attempt by engineers to do probablity 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).

6. Feb 17, 2005

### 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).

7. Feb 17, 2005

### gnome

8. Feb 17, 2005

### 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.

9. Feb 17, 2005

### Icebreaker

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

10. Feb 17, 2005

### 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.

11. Feb 18, 2005

### 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

12. Feb 18, 2005

### chroot

Staff Emeritus
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

13. Feb 19, 2005

### 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

14. Feb 19, 2005

### ramollari

15. Feb 19, 2005

### 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.