[tehsauce]

"Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1 both inclusive. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false."

Can someone explain how this is different than bayesian statistics?

[js8]

Bayesian statistics is one approach to modelling fuzziness and uncertainty, but fuzzy logic explores other approaches. For example, see https://en.wikipedia.org/wiki/Possibility_theory

Also fuzzy logic builds a "traditional" logical framework for deduction on terms, again this is a bit different from Bayesian approach, which is more abductive reasoning.

[tr352]

Apart from the other answers, there is also one important technical difference. Fuzzy logic is truth functional but probability is not. That is, in fuzzy logic, if you know the fuzzy truth value of A and of B, you can calculate the fuzzy truth value of “A and B” “A or B” and so on. Not in probability. If you know, let’s say, A and B both have probably 0.9, you don’t know enough to calculate the probability of “A and B”, which lies somewhere between 0.8 and 0.9, or “ A or B”, which lies between 0.9 and 1.

[elcomet]

Yeah but in the real world it doesn't matter does it?

you cannot compute the probability A and B for a reason: they might be related (what if they're mutually exclusive for instance? )

So how does fuzzy logic deals with this?

[tr352]

Fuzzy logic deals with this in the exact same way as classical logic. Note that in classical logic, the truth value of "A and B" and "A or B" is also a function of the truth values of A and of B. When using fuzzy logic you have to make a choice as to which function you use. Typically these functions generalise the classical logic ones in the sense that they behave like the classical ones when using 0 and 1. These functions are defined by a so called T-norm.

[lonelappde]

That's great in toy theory, like the formal real number system.

How useful is it for modeling real world problem?

[jacques_chester]

Very useful. Many problems are more easily represented as fuzzy sets or fuzzy relations than in other terms. It's particularly good at encoding linguistic variables, such as "very fast", "too cold", "accelerate hard" and so on in a way that it can smoothly overlap them.

It's also useful for encoding uncertainties that are not yet mutually exclusive. There are other logics too (eg Dempster-Shafer evidence theory), often grouped together as "monotone measures".

[dragonwriter]

> So how does fuzzy logic deals with this?

It doesn't, because truth values are not probabilities. They are answers to questions more like “How tall is X” than “How likely is it that X is sufficiently tall”.

[tomasGiden]

Did you wake up early this morning? Can you always answer that by a clear yes or no? When do you draw the limit between them? At 7:30? So if you woke up at 7:29:59 you would answer Yes and later No.

Instead you could put a distribution (but NOT a probability distribution) for belonging in the set of early that would look something like this.

If you wake up before 6:30 it would definitely 100% be early and at 8:30 it would. Or at 8:30 it would not at all, 0%, be early. Between there we would put some kind of partly belonging to Early rises.

In probability it is either or, but lack of knowledge makes us, but put a probability on what it is. In fuzzy logic, it is a bit of both at the same time.

[AstralStorm]

It's better to think of fuzzy logic like correlation in quantum superposition. As opposed to probability which is a different concept that maps to Bayesian logic.

Does not make it much easier to understand? You bet, which is why symbolic logic is much more useful.

[tlarkworthy]

Bayesian statistics has to follow Bayes rule. There is a fairly specific framework behind the numbers in Bayes (i.e. probability). Fuzzy logic is looser.

You could say Bayesian statistics is a subset of Fuzzy logic.

Given how informal people have to be in Bayesian statistics to come up with reasonable priors (e.g. uniform), and how well it works by just guessing reasonable values, it could be argued that the power of Bayes is not in the inference but from the slack in the system it permits. Fuzzy logic is pure slack.

I think modern neural networks with activations like leaky relu look more at home in a fuzzy logic textbook than in a statistics text book.

[jacques_chester]

> You could say Bayesian statistics is a subset of Fuzzy logic.

Arguably not. Mathematicians have teased out differences between different many-valued logics and systems. A critical one between probability and fuzziness is that probability includes the axiom of the excluded middle and fuzziness does not. In probability the values of mutually exclusive events must sum to 1.0, in fuzziness they need not, because it doesn't require events to be mutually exclusive in the sense that probability requires.

[tlarkworthy]

Yeah, Bayesian is a true model you can chop and change the viewpoint. It's much more sophisticated.

[tr352]

> You could say Bayesian statistics is a subset of Fuzzy logic.

I don't think that's accurate. Concepts like conditional probability and independence have no analogue in fuzzy logic.

[a_imho]

Back when I was in school neural networks, fuzzy logic and genetic algorithms were all taught in the same course called soft computing.

[regularfry]

Which is odd, because GA isn't like the others at all. We had a similar arrangement. I think the criterion wasn't "these things are similar in approach", more "these things are similar in lack of available rigour."

[AH2mdte8kPnJS]

Consider the likelihood of a dice that can land on both its ”1” side and its ”6” side at the same time?

Assuming that the die is fair, this is not possible in the real world.

Bayesian probability [1] states that this is not possible as expected.

``` P(land1 ^ land6) = P(land1) x P(land6 | land1) = 1/6 x 0 = 0 ```

However, fuzzy logic [1] results in an unintuitive result.

``` T(land1 ^ land6) = min(land1, land6) = min(1/6, 1/6) = 0 ```

[1] https://www.mathsisfun.com/data/bayes-theorem.html [2] http://www.sfu.ca/~jeffpell/papers/FuzzyLogic77.pdf

[cobbal]

As far as I can tell... Bayesian statistics is a model of the real world, fuzzy logic is just an easy to compute, bad approximation of reality that assumes everything is independent. (Someone correct me if I’m wrong; I’ve only studied logic and Bayesian stuff, not fuzzy logic)