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An Introduction to the Mathematics of Uncertainty (2010) [pdf]
- memming 8y agoNot Bayesian, that's Fuzzy!
- denzil_correa 8y agoIt 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
- soVeryTired 8y agoCan 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?
- wespiser_2018 8y agoFuzzy 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.
- soVeryTired 8y agoHave you got a concrete example?
- enriquto 8y ago> 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?
- finndark 8y agoenruquito 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.
- lou1306 8y agoI'm not able to do an 'elevator pitch' because I don't actually work with fuzzy logic, but the fact is... the concept itself is just not the same as propability. Compare these two statements: 1. The color of this apple is kind of yellow, but there's also a little red here and there. 2. This apple may be yellow with p=0.8, and red with p=0.2.
- finndark 8y agoFuzzy logic (FL) made it easier for control systems engineers to implement rule-based systems where rules were often extracted in human language from experts who had learned to manually control the systems. The Japanese were quick to adopt FL and benefited enormously financially. Now FL is embedded almost everywhere. Michio Sugeno built a fuzzy logic control system that flies a helicopter with a rotor blade missing! It is possible to do that with a conventional control system (that is, a mathematical solution must exist), but I believe the mathematics might be a bit more difficult.
- wespiser_2018 8y agoGreat book! Getting folks to understand statistics and data in terms of uncertainty is always a challenge!
- yakubin 8y agoOT but the fonts are awful, the title page isn't even centred properly, figures lose quality when zoomed in... Just use LaTeX, people.
- rcap 8y agoActually, this was made with LaTeX. Sadly, LaTeX doesn't prohibit you from making ugly documents.
- yakubin 8y agoOh... My bad.
- capnrefsmmat 8y agoThe title page isn’t supposed to be centered — this is typeset for double-sided printing, where one edge of the paper will be in the binding and hence inaccessible. It’s standard typesetting practice to have asymmetric margins to account for this, and you can see it in all subsequent pages as well. I do agree, though, that using a math font that doesn’t match the text font is a high typographic crime.
- ginnungagap 8y agoThe different margin sizes on the left and right (swapped between odd and even numbered pages) are the standard for the book documentclass in LaTeX because that's the best for printing and binding!