[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."