5 ms·

Not my recollection and I gave a lecture on it (in 1987): https://web.archive.org/web/20081202004655/http://web.onetel.com/~hibou/ai-course/lec02.txt https://we

Not my recollection and I gave a lecture on it (in 1987): https://web.archive.org/web/20081202004655/http://web.onetel.com/~hibou/ai-course/lec02.txt https://web.archive.org/web/20081202004655/http://web.onetel... There are crisp sets, such as the set of French people. People are either French or not French. It doesn't make sense to say that someone's not very French, for example. But it does make sense to say that there's an 80% chance that someone's French, given other information about them. The set of tall people is a fuzzy set. It does make sense to say that someone's not very tall. Tallness is a mapping from height to degree of membership of the set of tall people. So, for example, tallness(1.6m) = 0.0, and tallness(2.0m) = 1.0. To find out whether someone's quite tall, you could use the square root of tallness,to find out whether someone's very tall, you could use the square, and to find out whether someone's not tall, you could subtract their tallness from 1.0. And you might want to put a value on whether someone's quite tall but not very rich, for example, or make deductions given this. Maybe at some deeper level fuzzy logic does reduce to probability theory, but the idea is quite different. It's about vagueness rather than about uncertainty.

whatshisface 7y ago
Maybe that example could be reduced to probability by saying you had an ensemble of different classifiers, each with its own hard cut. Then, you would ask, "what is the probability that a randomly selected judge would call Sally tall?"
- DonaldFisk 7y ago
  Yes, that's what I was hinting at.
- jacques_chester 7y ago
  This doesn't really reduce it though, it just changes the problem from degree-of-tallness to probability-of-opinion. If I round up a million and people and survey them about whether -1, 0 and 1 are natural numbers, the probability of their opinions don't change whether -1, 0 or 1 are natural numbers. The probabilities of judgement might be 0.1, 0.55 and 0.92, with confidence intervals. But each of these numbers has a set membership function and each of them is crisp. In fuzzy sets these belong to the set of natural numbers as 0.0, 0.0 and 1.0. The useful concept that fuzzy sets brought to the table was being able to reason formally over uncertain values. Classical logic operates on crisp sets: all men are mortal, Socrates is a man, therefore Socrates is mortal. Fuzzy sets allows you to retain all the tools of logic over a wider range of statements. This is widespread in control systems, where being able to reason formally about vague concepts like "too fast" is very helpful. It's also common in caselaw, which is absolutely jampacked with fuzzy sets. "The purchaser at arm's length without notice". "The reasonable person, similarly circumstanced". "A duty of care". Different sets of facts in a case are ultimately resolved into binding rulings by a judge, but the argument itself has to follow logically from facts, legislation and precedent. The law is also rightly aware of probabilities, especially in civil cases. "The balance of evidence" is sometimes called "the balance of probabilities". In criminal trials, "beyond reasonable doubt" is mostly about deciding on what follows from the probabilities of the facts presented.
jrumbut 7y ago
I've heard it said that probability is quantifying the uncertainty you have about an outcome, fuzziness is knowing the outcome and quantifying your uncertainty about what to call it.
FrozenVoid 7y ago
> People are either French or not French. It doesn't make sense to say that someone's not very French, for example. Genetics exists.
- checkyoursudo 7y ago
  >> People are either French or not French. It doesn't make sense to say that someone's not very French, for example. > Genetics exists. What would you mean if you said that someone is genetically French?
  - FrozenVoid 7y ago
    You can take a genetic test(e.g. 23andMe) and determine the % of French genes. Or if you believe genes are a social construct read https://www.usnews.com/news/best-states/north-carolina/articles/2019-06-03/race-impedes-bid-for-bone-marrow-transplant-for-3-year-old https://www.usnews.com/news/best-states/north-carolina/artic...
  - FellowRedditor 7y ago
    Genetics is a racist pseudoscience pushed by white males. It has no meaning whatsover, French are a social construct.
- sonnyblarney 7y ago
  'French' is more a culture than a genetic diaspora (i.e. though most French people might have some genetic 'closeness' that distinguishes them from other groups, one does not need that genetic approximation to be French) And it's perfectly reasonably to say someone is 'not very French'. I lived in France, I speak French fluently, and could 'get by' as a French person, but it would be fair to say that I am 'not very French'. I think Fuzzy logic, as a perspective, maybe should be appreciated. I can be 'a little this and a little that, and mostly some other thing' - it makes sense to describe many things as such. Though pragmatically, when it comes down to numbers ... it may simply look a lot like probability.
  - 7y ago

whatshisface 7y ago

Maybe that example could be reduced to probability by saying you had an ensemble of different classifiers, each with its own hard cut. Then, you would ask, "what is the probability that a randomly selected judge would call Sally tall?"

DonaldFisk 7y ago
Yes, that's what I was hinting at.
jacques_chester 7y ago
This doesn't really reduce it though, it just changes the problem from degree-of-tallness to probability-of-opinion. If I round up a million and people and survey them about whether -1, 0 and 1 are natural numbers, the probability of their opinions don't change whether -1, 0 or 1 are natural numbers. The probabilities of judgement might be 0.1, 0.55 and 0.92, with confidence intervals. But each of these numbers has a set membership function and each of them is crisp. In fuzzy sets these belong to the set of natural numbers as 0.0, 0.0 and 1.0. The useful concept that fuzzy sets brought to the table was being able to reason formally over uncertain values. Classical logic operates on crisp sets: all men are mortal, Socrates is a man, therefore Socrates is mortal. Fuzzy sets allows you to retain all the tools of logic over a wider range of statements. This is widespread in control systems, where being able to reason formally about vague concepts like "too fast" is very helpful. It's also common in caselaw, which is absolutely jampacked with fuzzy sets. "The purchaser at arm's length without notice". "The reasonable person, similarly circumstanced". "A duty of care". Different sets of facts in a case are ultimately resolved into binding rulings by a judge, but the argument itself has to follow logically from facts, legislation and precedent. The law is also rightly aware of probabilities, especially in civil cases. "The balance of evidence" is sometimes called "the balance of probabilities". In criminal trials, "beyond reasonable doubt" is mostly about deciding on what follows from the probabilities of the facts presented.

jrumbut 7y ago

I've heard it said that probability is quantifying the uncertainty you have about an outcome, fuzziness is knowing the outcome and quantifying your uncertainty about what to call it.

FrozenVoid 7y ago

> People are either French or not French. It doesn't make sense to say that someone's not very French, for example. Genetics exists.

checkyoursudo 7y ago
>> People are either French or not French. It doesn't make sense to say that someone's not very French, for example. > Genetics exists. What would you mean if you said that someone is genetically French?
- FrozenVoid 7y ago
  You can take a genetic test(e.g. 23andMe) and determine the % of French genes. Or if you believe genes are a social construct read https://www.usnews.com/news/best-states/north-carolina/articles/2019-06-03/race-impedes-bid-for-bone-marrow-transplant-for-3-year-old https://www.usnews.com/news/best-states/north-carolina/artic...
- FellowRedditor 7y ago
  Genetics is a racist pseudoscience pushed by white males. It has no meaning whatsover, French are a social construct.
sonnyblarney 7y ago
'French' is more a culture than a genetic diaspora (i.e. though most French people might have some genetic 'closeness' that distinguishes them from other groups, one does not need that genetic approximation to be French) And it's perfectly reasonably to say someone is 'not very French'. I lived in France, I speak French fluently, and could 'get by' as a French person, but it would be fair to say that I am 'not very French'. I think Fuzzy logic, as a perspective, maybe should be appreciated. I can be 'a little this and a little that, and mostly some other thing' - it makes sense to describe many things as such. Though pragmatically, when it comes down to numbers ... it may simply look a lot like probability.
- 7y ago