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Hi, from what you have read or heard about, which is a good book on fuzzy logic/sets/systems? I'm interested in basic of fuzzy systems, fuzzification/defuzzification etc. Thanks, Lucian
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You might try to learn some of the basics with Bart Kosko's book on Fuzzy Thinking, is more on the philosophical side of the equation, rather than in the technical side, but it might work.
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Thanks. However, the reviews from amazon do not look very appealing: http://www.amazon.com/Fuzzy-Thinking-New-Science-Logic/dp/0006547133/ref=sr_1_1?ie=UTF8&qid=1292848830&sr=8-1
(Dec 20 '10 at 07:41)
Lucian Sasu
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Actually Kosko was a student of Zadeh (the creator of fuzzy logic) and he always says Kosko is his successor in this field, the reason of the reviews is because people look for a textbook and it is not a textbook
(Dec 20 '10 at 08:33)
Leon Palafox ♦
Isn't a textbook what the OP was after?
(Feb 02 '11 at 08:38)
Will Dwinnell
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He asked for a book with the basics, and that book has the basics from a non mathematical point of view, is very good to grasp what fuzzy logic is all about.
(Feb 02 '11 at 08:41)
Leon Palafox ♦
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If you want to implement a fuzzy logic system, I suggest "The Fuzzy Systems Handbook" by Earl Cox. If you want a more theoretical knowledge of fuzzy logic, I'd recommend "Fuzzy Sets and Fuzzy Logic" by Klir and Yuan, or "Fuzzy Sets, Uncertainty and Information", by Klir and Folger. I would avoid Kosko.
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You might wish to try: An Introduction to Fuzzy Logic for Practical Applications. It has decent reviews at Amazon as well: http://www.amazon.com/Introduction-Fuzzy-Logic-Practical-Applications/dp/0387948074/
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so many downvotes... but why? why?
Could someone please explain to me why one wants to use fuzzy methods? I took a little look at the math behind it and I don't understand why one might want that. What's wrong with good old probability theory? I tried to talk to fuzzy people on WCCI last year but I found no one (of course I didn't talk to the big shots with such a trivial question) who new about fuzzy and probabilistic methods.
I guess that probability theory cannot handle linguistic variables. Or, at least, I do not know about such an approach. How do you model "Jane is pretty tall" with probabilities? How do you model "If temperature is low, then increase gas flow?" and so on? We are not talking about degree of belief or smth that probability theory can handle (afaik).
What do you mean by degree or belief? Probabilistic methods are just a mathematical formalism. They are often used in practice to model ambiguities and uncertainties. I am not quite sure what "Jane is pretty tall" means... compared to whom? Of course you could model the distribution over all people or all females or something and then let the size of Jane be a distribution that has a lot of mass on the right sight of the Gaussian. And about the second one, I don't see any problem at all. I would model this as a linear Gaussian. But I find this argument pretty much beside the point any way. Where do these sentences come from and how did you parse them? What do you want to do with these sentences? If I want a system to "increase gas flow if temperature is low" then I don't want a fuzzy explanation. I want my system to learn exactly what to do at a given temperature. So this sounds like a reinforcement or maybe regression problem.... Cheers, Andy
Degree of belief: see Judea Pearl's books, e.g. http://books.google.ro/books?id=AvNID7LyMusC&pg=PA17&dq=%22degree+of+belief%22+judea+pearl&hl=en&ei=6H8PTYW-JpCJ4gaax6CGAg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCcQ6AEwAA#v=onepage&q&f=false . And "Jane is pretty tall" is a very common fuzzy statement, which occur in day-by-day communication. Of course, it's uncertainty, but I am not so sure for the moment that probability theory can handle all types of uncertainty. Maybe the linguistic fuziness might be a more productive approach. Finally, "increase gas flow if temperature is low" is from "Computational Intelligence: Concepts to Implementations" where it is shown how by fuzzyification and defuzzification one can obtain a concrete numerical value that is finally fed into a gas regulator.
I guess that there is the old debate, "is fuzzy logic a good approach to handle some forms of uncertainty", or "is fuzzy logic legitimate"? In practice, FL is shown that "it works". No doubt, probability theory and statistics, being mathematically supported, are good approaches, but I seriously doubt that they are omnipotent approaches. What is your opinion?
Maybe I should a little more at the literature. Thanks for pointing out these examples. But given these sentences, it's really not clear to me what you want an algorithm to do. An example that was given by Tenenbaum about probabilistic methods for modeling uncertainty in language, was the following setup: A question of the form "You waited in line for 5 minutes. How long do you still have to wait?" were posed to human test subjects. And the same sentence/question pairs were given to a Bayesian probabilistic model. It turned out that humans and the Bayesian model deal with uncertainty in the same way and both give the same answers. Here, it is clear what the task was: Give a numeric answer. What is the task in the sentence "Jane is pretty tall" ?
"Jane is pretty tall" allows one to establish the degree of membership to the set of tall women as being 0.8 (say... depend of my culture; nordic women are taller, so this number can be a little large/smaller).
Hence, a numerical value is obtained and can be feed in a clustering algorithm, or can be used as input in an artificial neural network. It allows one to compare different persons regarding their height. How could you do it with probability or probability density functions? this is not obvious for me.
"An example that was given by Tenenbaum" - that's interesting. Could you give the title of the article/URL/smth for this reference? Thanks.
This particular example is from http://web.mit.edu/cocosci/Papers/Griffiths-Tenenbaum-PsychSci06.pdf though I haven't read the paper. But I think there are several other works by him in this direction. There is this paper "how tall is tall" http://www.mit.edu/~lschmidt/papers/cogsci2009_final.pdf that seems to relate to this discussion ;) This one does not really relate to this discussion but is quite nice. At least the overall picture. Its a bit lengthy http://web.mit.edu/clbaker/www/papers/cognition2009.pdf
Back to "Jane is pretty tall": So you hand pick the value 0.8. And if "Tiffany is pretty tall" then does she get the same number? And what does this numerical value mean? It seems not to be how tall Jane is. So it is some feature of Jane that is not clear how to interpret and that you set arbitrarily. That does not seem very helpful to me.
What I think the obvious question about that sentence is, that your system does not answer is "How tall is Jane?" My suggestion was "Of course you could model the distribution over all people or all females or something and then let the size of Jane be a distribution that has a lot of mass on the right sight of the Gaussian" (see above) And how to obtain a value from this? Just take the expected value. Of course I described this distribution not very precisely. But that is not really possible since there is nothing in the sentence that lets you know how it is supposed to look. The real method to find a numerical value is to learn from data what people mean by tall. So you show them 100 people and ask them whether the people are tall or not and then you model the answers (maybe conditioned on the rated peoples ethnicity, age and gender). Then you know what tall means. And when I look again at the sentence, I can calculate the expected value of Jane's height, knowing that she is tall and female. And if I want, I can also model the distribution of how probable it is that someone who is called Jane belongs to a certain ethnic group and use that to enhance my prediction. And now I know how tall Jane probably is. And I also know how uncertain I am about how tall she is. I think that is all I can ask for.
W.r.t. "increase gas flow if temperature is low" it always felt pretty bogus to pretend this is a fuzzy logic statement. In the end you're just tacking on statements like "low for temperature is between 0 and 15" and then turning this into hand-coded rules that you have no guarantee should work or even make sense, specially since there will be lots of parameters all over the place that interact nonlinearly only with the grounding provided by some ill-specified intuition about the problem. And about the original statement, I don't see how it can be more meaninful than "if (temp < 15) increaseFlow();".
@Alexandre Passos: "low" and "increase" are fuzzy terms. Of course that finally they are translated into precise numerical values, but what is "low temperature" for me might be "comfortable" for you, hence in the first stage one avoids hardcoding the rules. This is not so substantial, but I like abstractions at the first stage.
Second: there might be multiple rules, somewhat contradictory. See the book "Computational Intelligence: Concepts to Implementations" for a broader example with temperature and gas regulators. There, a lot of fuzzy rules are fired and some of them might sound contrary to the others. While contradictory rules are not supported in binary logic, they are fine for fuzzy systems and still lead to useful results. What do you do if in a classical rule based system you have both "if (temp < 15) increaseFlow();" and some opposite rule? It seems that allowing for apparently contradictory rules is a good point of fuzzy systems. Of course, this should not lead to chaos and full contradiction.
@Imsasu about contradictory rules, what I feel is that in the end if one rule says "set flow to 5 if temp < 15" and another rule says "set flow to 50 if pressure > 10", and for some unspecified reason temp < 15 and pressure > 10, there are some options about how to act, and some systems will blow up if you choose the incorrect rule (or the wrong midpoint between them), and probably the person who wrote the rules should know what is the safe action to take, and that should be clear in the rule-based system, or a priori some systems will work and others won't. I don't see how arbitrarily breaking ties is always beneficial, unless the tie-breaking mechanism is well understood, and when you have hundreds of variables interacting nonlinearly I don't think it can be that easily understood.
@ Alexandre (second last, your to fast for me ;) My feeling exactly. And you put it a lot more simple than I did :) In the end, what I said about Jane above boils down to (hight Jane) > (average height) if you don't know anything else.
And if you want to know more, probability theory gives you the tools to learn more and specify how your knowledge influences your decisions.
@Andreas Indeed I've been following the thread and you also expressed how I feel about the "pretty tall" thing. I really don't see it as a matter of a real-valued membership to a binary property no matter how you present it, and fuzzy logic seems to "solve" semantic problems by pretending they're solved, which never made any sense for me. I also think people interested in this should read Tanenbaum's work.
@Andreas Mueller: Thanks for references. "Tiffany is pretty tall" should lead to the same value, otherwise the fuzzy membership values would be inconsistent and useless. Afaik, there is no way for someone using fuzzy systems quantify the uncertainty as it is done in statistics or probability theory.
I guess the ask for a good fuzzy systems book is now stringent. Based on comments above, I would like to see a critical comparison of probability theory vs fuzzy systems. What types of problems can be solved better by FS than by probability theory? One can see a lot of articles where FS are used to solve some particular problems, but I did not encounter one discussing if there is an alternative approach based on fuzzy logic. Hence, the initial query of the question should be restated as ".. a book/article showing the effectiveness of fuzzy systems compared to some alternative approaches".
I would be very much interested in that, too. I saw a lot of work on fuzzy systems on WCCI but never a comparison. And none of the people I talked to were very interested in one. My first comment was in the same direction. Many people say "It's just a matter of taste" but I don't find this particularly satisfying. Maybe we should post this as a new question ;)
@Andreas: "Maybe we should post this as a new question ;)" - be my guest.
Fuzzy set membership is not the same thing as probability. In probability theory, set membership is absolute: a thing is defined as either a member any given set, or not. With fuzzy sets, membership is graded.
For instance, when I stand in the doorway between the kitchen and dining room, it may be useful to assign a degree to which I am a member of the set of things "inside the kitchen". When I am nowhere near the kitchen, that membership is 0.0, when I am in the center of the kitchen, that membership is 1.0. When I stand with half my body in the kitchen, me might assign a membership of 0.5. Unlike a probability, this partial membership will never be resolved by some revealing event, such as a coin toss.
This comment thread might not be the best place for this discussion but anyway: 1) You say that in fuzzy set theory, membership is graded. But this only means that there is a continuous function on defined on the set, which you call "membership". In probability theory, it's called probability mass (well, it's a little more complicated than that. Actually it's a measure on a sigma-algebra but that's not so important here). 2) Wouldn't in your example a function giving "distance from kitchen" being a more natural choice to describe the situation? 3) Probability theory has nothing to do with some "revealing event". It is about measures and measureable function and lots of integrals ;) It's just a mathematical framework. It is often used to model "random events" and uncertainty in the real world, for example in cases of incomplete information. But that has nothing really to do with the math.
You continue to equate fuzzy set membership with probability, which I have explained are not the same thing. If you are that uncomfortable with fuzzy sets I suggest that you do not use them.