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Fuzzy Logic

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Re: Fuzzy Logic

#41
post #8

"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?

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

Re: Fuzzy Logic

#43

Earlier quoted context omitted.

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…

> 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 doe…

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