
An Introduction to the Mathematics of Uncertainty (2010) [pdf] - headalgorithm
https://www.creighton.edu/fileadmin/user/CCAS/programs/fuzzy_math/docs/MOU.pdf
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denzil_correa
It is important to distinguish between risk and uncertainty.

> "Uncertainty must be taken in a sense radically distinct from the familiar
> notion of Risk, from which it has never been properly separated.... The
> essential fact is that 'risk' means in some cases a quantity susceptible of
> measurement, while at other times it is something distinctly not of this
> character; and there are far-reaching and crucial differences in the
> bearings of the phenomena depending on which of the two is really present
> and operating.... It will appear that a measurable uncertainty, or 'risk'
> proper, as we shall use the term, is so far different from an unmeasurable
> one that it is not in effect an uncertainty at all."

[https://en.wikipedia.org/wiki/Knightian_uncertainty](https://en.wikipedia.org/wiki/Knightian_uncertainty)

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kgwgk
The concept was popularized a few years ago by Rumsfeld with his "known
unknowns" (risk) and "unknown unknowns" (uncertainty).

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soVeryTired
Can anyone give a high level summary of what you can accomplish with fuzzy
logic that you can't do with more classical probability theory?

What's the 'elevator pitch' for why someone should learn the theory?

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wespiser_2018
Fuzzy sets allow you to use set theoretic tools over objects with varying
degrees of membership. This is a useful construct when trying to reason over
probabilistic evidence, and IMO can be a useful modelling tool.

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enriquto
> set theoretic tools over objects with varying degrees of membership

you can also do exactly that in probability theory by multiplying the
probabilities. Is there any difference?

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finndark
enruquito says>"you can also do exactly that in probability theory by
multiplying the probabilities."

Have you got a concrete example?

i.e., show us the probability version precisely with mathematics and maybe
someone can tell you the corresponding fuzzy version, if any.

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memming
Not Bayesian, that's Fuzzy!

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yakubin
OT but the fonts are awful, the title page isn't even centred properly,
figures lose quality when zoomed in... Just use LaTeX, people.

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rcap
Actually, this was made with LaTeX. Sadly, LaTeX doesn't prohibit you from
making ugly documents.

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yakubin
Oh... My bad.

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wespiser_2018
Great book! Getting folks to understand statistics and data in terms of
uncertainty is always a challenge!

