Ask HN: What happened to fuzzy logic? Fuzzy Logic was a very talked about field few decades ago. What is the state of that field of research? Is it still being persued or are there applications of it already implemented commercially? |
Ask HN: What happened to fuzzy logic? Fuzzy Logic was a very talked about field few decades ago. What is the state of that field of research? Is it still being persued or are there applications of it already implemented commercially? |
If you want to take a system that's working on Boolean logic, and introduce uncertainty, replacing true/false with probabilities does a great job of this. However in the 1960s/1970s, people believed it was hopeless to have AI systems use probability to deal with uncertainty. This is because probability requires you to use Bayes' Theorem, and computing the denominator in Bayes' Theorem requires summing over an exponentially large number of different outcomes.
Thus people came up with all kinds of alternative systems to avoid dealing with probability. Among these would have been fuzzy logic.
However people came up with ways to cope with the computational intractability (belief propagation on Bayesian networks, better Markov-chain Monte Carlo algorithms, etc.), so probability became practically viable. And on the merits, if you can deal with the computational issues, probability seems to be much nicer than these other formal systems. So since the 1980s/1990s the probabilistic approach to AI has become dominant (even if deep learning has displaced the actual models).
>replacing true/false with probabilities does a great job of this ... people came up with all kinds of alternative systems to avoid dealing with probability
a probability is a number between 0 and 1, instead of either 0 or 1. a number between 0 and 1, instead of 0 and 1, is called fuzzy logic.
so I'm really lost about what you're saying here.
Numeric representation may be the same[0], but the rules of how to do math on them, and what that math means, are different.
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[0] - AFAIK dealing with Bayesian math, it's usually more useful to take a logarithm of all probabilities, so you can add them instead of multiplying. This translation expands the range from <0, 1> to <-infinity, +infinity>, and incidentally makes it clear why some people say that "zero and one are not probabilities".
[0] Not necessarily. You might choose to measure X that way, but it's not required.
It is common to saysthat the 'truthiness' of (a and b), is the minimum truthiness of a and b. Or becomes a maximum, not becomes 1 - truthiness. Then normal predicate logic works by combining these rules the usual way. E.g. (a implies b) becomes b or not a, which is max(b, 1-a).
Basyan probability is much more sophisticated, but also more difficult to calculate.
Fuzzy didn't go very far because it could already be implemented back then with cheap processors (we had Moore's law!) and some slap-on programming. Or domain-specific logic hardwired by engineers who knew what the outcome should be given a bunch of inputs: think "balancing robot" or washing machine torque control.
Modern ML and powerful Arduinos make fuzzy logic irrelevant today, except that Markov chains should also be irrelevant but they aren't, so who knows, maybe fuzzy could stage a come back. Despite its huge limitations, FL certainly is better than current neural nets when it comes to transparency so that humans can better visualize what it's doing. Disclaimer: back in the day I built a "FL tracker" in Visual Basic so that you could visualize the full system trickle-down a decision in realtime and it was very enlightening. Today I'd love to build the same visualizaer but for LLM generation!
Fuzzy Logic has some utility in engineering applications, because it can be intuitive for humans interpret and to create rules using it. Interpretability is also the strong point of neuro-fuzzy logic (hybrid system). Applications are usually control systems, business logic, or embedded systems with tight resource constraints.
(negatives:)
In academic research it's not that interesting, because it's just one multi-valued logic among others, subset of infinite-valued logic. It's not very useful in machine learning because there are no efficient way to learn fuzzy rules automatically.
Thruly, tho look at things like QAM encoding schemes and the tricks stepper motor controllers are doing. We have found ways to analog-ize a lot of things that were formerly viwed as totally digital; which i think is what the "fuzzy logic" hype boiled down to anyway.
At least my recollection of fuzzy logic are from around the late eighties / early nineties and always involved the example of a thermostat that can only turn fully on or fully off. :)
The reason why researchers on neural networks started to talk about "deep learning" in the 2000's is because neural networks had a bad press and articles were being rejected. Machine learning on the other hand was hot so it was a way to get their papers accepted.
When I'm drawing on screen and placing a widget not on the left or the right, but at x=f*width, is that already fuzzy logic? The classical examples of Japanese washing machines determining detergent dose are not much more complicated.
Fuzzy logic was in favor to the relative new field of neural nets (ML as we know it today). Because from the limitations in industrial control neural nets were too costly. Yes, we had already things like the first i386embedded. But that was way too expansive. Most of the PLCs were based on 16-bit microcontrollers and even those were more on the expansive side.
So if you think commercially in terms of industrial control systems, then Fuzzy Logic was implemented and used. I assume old systems can be found anywhere even today. Remember that in industrial control 20 years is no time.
Today, everybody in industrial control is also about ML. But here again, that is still on the expansive side. Such Nvidia Jetsons do not come for cheap.
Among the more philosophically inclined, there was controversy other whether fuzzy logic was really something new or just a repackaging of old ideas with a misleading vocabulary. There was a book on how this debate played out in journal articles, but I can't think of the title now.
† one speculative use would be to assign degrees(?) of agency, some kind of a future unit of measurement: a person can be 100% evolved, or maybe 49% evolved and 51% designed (prosthetics, neural implants, and so on).
[1] https://en.wikipedia.org/wiki/Characteristica_universalis
[2] 2017, Fuzzy Dual Numbers: Theory and Applications, https://dl.acm.org/doi/book/10.5555/3172931
[3] "Fuzzy Dual Dynamic Programming", https://hal-enac.archives-ouvertes.fr/hal-01372543/document
[4] "Dual Numbers & Automatic Differentiation", https://blog.demofox.org/2014/12/30/dual-numbers-automatic-d...
The first, is the true fuzzy logic, which consists of Fuzzy Set theory and Fuzzy Measure theory. The two are distinct but interrelated, and heavily mathematical in nature. In particular, Fuzzy Measure theory completely subsumes Probability theory (i.e. probability theory is a strict subset of fuzzy measure theory, and therefore anything that can be expressed in probabilistic terms can be expressed in equivalent fuzzy measure theory terms, with leeway for added generality).
The second, is a class of techniques, based on Fuzzy Set / Fuzzy Measure theory, which implement some very simple behaviours which allow you to solve a particular class of problems. This is the standard Sugeno/Mamdani logic, fuzzy inference as the application of a few straightforward rules for conducting conjunction/disjunction among fuzzy rules.
The first is still thriving, but largely in the theoretical realm.
The second is shunned, on the basis that it feels like a bunch of interpolation heuristics, and a Bayesian approach is usually "better", even if not as intuitive of straightforward.
Unfortunately this has had a self-prophetic impact, in the sense that any literature which would have been better described as fuzzy, is labelled as probabilistic, even if strictly speaking the concepts involved are not strictly-speaking probabilities, but should more correctly have been addressed as fuzzy measures.
Personally I have published papers where I had to "disguise" fuzziness as probability just to get it considered for publication, or where I had to "apologize" for the term, or making it explicit that fuzziness in this context is unrelated to this set of tools that is typically thought of as "the fuzzy approach".
Having said that, one area that is thriving is the use of Fuzzy methods in the context of more general AI / NeuralNetwork methods, particularly in the context of explainability. Type 2 Fuzzy methods in particular (which introduce one or more layers/dimensions of fuzziness/uncertainty over the membership function itself) are quite an active area of research.
Finally, there are some frameworks that borrow heavily from fuzzy theory, but strictly speaking are independent. The one that interested me the most in recent years was "Subjective Logic", proposed by a guy called Audun Jøsang; this sounded like a very interesting logic framework and I was very keen to use it in my work, but in the end I just didn't have the time to justify that investment ... It's worth looking up though. The basic idea is that you have a framework where you have rules that have a built-in way of carrying uncertainty with them, with a one-to-one mapping with beta probabilities over your fuzzy-like rules, and a set of logical operations (which map to the usual logical operators) that are adapted to carry the uncertainty with them. This means that you can reduce your problem into a set of simple logical statements, and the framework would then take care of the uncertainty calculations for you seamlessly.
Is it fuzzy logic because there is presumably hysteresis in the water heating phase?
Or is it fuzzy in the way to converts turbidity of water to wash times?
I remember reading about dedicated fuzzy logic circuits which essentially gave you simple fuzzy state machine programmed with cheap ROM, and it was all you needed instead of MCU for many tasks.
In a way cheap powerful MCU are biggest killers of the technique.
There is a particular logic (“Classical Logic”) that people are usually thinking of when they mention logic. Many folks don’t know that there are many, many logics that have been invented by mathematicians and philosophers, and an infinity of possible logics. All are as mathematically sound as each other. They vary in how truth behaves (SQL’s true-false-null is a poor attempt at a 3-valued logic, for example; or you might include notions like necessity and possibility or time).
Fuzzy logic is another logic. It’s quite precise about how truth behaves, and truth is a real number on the range [0, 1]. And it does a nice job of providing a notion of partial truth.
Unlike boolean logic where you're either "tall" or "not tall".
But, it's probably a bit out of date by now.
Also, if you'd like to learn more about Type-2 Fuzzy Systems, look up anything by Hani Hagras (disclaimer: colleague of mine from the same university, but highly regarded in this field)
For example, surreal numbers are much more expressive than reals, and there are ways to express gaps as first order concepts (although not strictly a number) that maps very well to this space. I just skimmed through Audun Jøsang paper and the ideas of Belief/Disbelief to represent uncertainty resonates with Conway's construction of surreal numbers quite a bit.
fuzzy logic is not binary, but multimodal/range. what maps unto that today? probability on top of layered NN, aka deep learning. It's no coincidence that no one knows how the deep learning models "think." They are by design very fuzzy.
Using your example, if the control system can utilize non-binary, numerical input and do something with it in actuators, then just give it the actual height (in cm). If it can't, then introducing the concept of "semi-tall" isn't going to be helpful.
The example we learned in class is the classic thermostat of an air conditioner. Sure, it would be nice if it can tell between cold, warm and hot instead of a binary 0 and 1, but why not just use the actual numeral value (0.1, 0.22, etc.) then?
The aircon example isn't really that great, to be honest, because there's only one rule and only one action you can take. If you add in "how full is the room" (and letting that be tuned for room size), an automated window vent, the outside temperature, and some sort of air quality reading, you can see how the job of making a room tolerable to be in starts to combine factors in interesting ways. https://en.wikipedia.org/wiki/Fuzzy_associative_matrix and https://en.wikipedia.org/wiki/Defuzzification are things I'm sure your course would have covered, but that's where I'd point at as a start.
When you say that "The hotel room is 75% clean", that's a degree. It means a room that's not as clean as a "90% clean" hotel room, but definitely cleaner than a "50% clean" hotel room on some kind of cleanliness scale that you have. You need a scale because the boundary between clean and unclean is not sharp, but fuzzy. Fuzzy logic gives you tools to construct well-behaved scales for logical combinations of variables that already have scales associated with them. E.g. if you have a scale for a motorcycle being loud and a scale for a motorcycle being expensive (both fuzzy concepts), the tools of fuzzy logic can e.g. give you a scale for loud OR expensive.
In contrast, when you say that "The hotel room is clean with probability 75%", you're reasoning about how likely it is that the room is clean under uncertainty. Maybe the cleaners only work 3 out of 4 days, and you're unsure what day it is. But these are not degrees of cleanliness: if you say that a room has a 75% chance of being clean you're not claiming that it's cleaner than some other room that has a 50% chance of being clean.
The concepts involved in probability need not be fuzzy, or even measured on a scale. E.g. when one says "there's a 75% chance that the car repair will cost more than $50", there is no fuzziness involved in whether the repair costs more than $50 or not: in the end, you'll get a bill, and it will state a number that is unambiguously either above $50 or not above $50, a pure binary variable, no scales involved.
Probability: “There’s a 70% chance the grass will be wet tomorrow morning”
Fuzzy logic: “The grass will be 70% wet tomorrow morning”
x AND y is xy, x OR y is x + y - xy
Whereas in (Zadeh) fuzzy logic:
x AND y is min(x, y), x OR y is max(x, y)
IIRC, “fuzzy logic” is actually a class that includes all generalizations of crisp binary logic to continuous values over [0,1] with operators meeting a set of definitions which basically boil down to “reduces to crisp logic when the input values are constrained to 0 and 1”, so that Bayesian logic is a fuzzy logic.
The Zadeh operators in particular I remember being constructed, or at keast rationalized, as ways to combine the degree of truth of propositions as distinct from the probability of truth of uncertain proposition. But I think interest in the kind of epistemic differences in alternative extensions to propositional logic faded with the lack of a practical need in terms of computational efficiency to avoid Bayesian probability (and I think there was also a separate philosophical battle and the side in favor of “Bayesianism is the only meaningful extension of propositional logic” was winning that battle when the computational problems were resolved, which helped sweep aside the alternatives.)
No it isn't. P(x AND y) = P(x)P(y) only in the special case where x and y are independent. Unlike fuzzy logic, probabilistic logic is not truth functional.
You are obviously correct, and I shouldn’t post when I should be sleeping.
> Unlike fuzzy logic, probabilistic logic is not truth functional.
Its been a long time since I had much engagement with fuzzy logic, but I distinctly remember it being constructed as a class such that Bayesian probability was a fuzzy logic, though the others of interest were much simpler. But that may be as wrong as the other part of that post...
I don't think that would work for clothes washers though, because there isn't the same kind of pumping water for recirculation. Somewhat related, my washing machine (upright, high efficiency) measures the load by spinning it with a calibrated input impulse and measuring the rotation of the basket, less rotation means more clothes means more water. It's helpful to load the clothes around the edge to get the right amount of water. But that doesn't illuminate how cycle duration is determined.