Talk:Fuzzy logic

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I would also strongly support the point of view that fuzzy logic must not be separated from prob theory. This is due to the fact that conditional on some covariate (e.g. position in the house) membership fractions add to one, which simply can be interpreted as a multinomial distribution. The point of confusion might be that this is a conditional distribution and no distribution of the covariate is usually assumed. The question is just whether inference differs in fundamental way. I cannot see this either, but maybe I am missing something. Any functional depending on membership fractions/probalities should be interpretable in a statistical sense (predictions, moments, moments of functions, etc.). I think this needs to be clarified. Sboehringer 10:40, 31 December 2006 (UTC)

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[edit] Older discussion

Much as I respect the important contributions of Dr. Lofti Zadeh in the '60s, particularly in the reduction of an idea to engineering practice, the roots of fuzzy logic lie in the concept of "vagueness." My father Max Black published one of the seminal papers on this concept before WWII - cit.: Philosophy of Science 4, 427-455, Oct. 1937. I have brought this to Dr. Zadeh's attention and he recognizes its precedence. adamsmithusa

then you should add this information to the article, perhaps in a section on the history of the concept.--Scriber 02:55, 15 August 2005 (UTC)

Fuzzy logic describes a specific type of multi-valued logic which has gained considerable application in engineering. It warrants an article on its own, IMHO. --Robert Merkel

Fuzzy logic is used to control household appliances (such as washing machines which sense load size and detergent concentration and auto-adjust their wash cycles accordingly; and refrigerators)

I'm not sure about the washing machines. It's not logic - it's just using the load size to calculate the detergent concentration. There is no predicate in that. The system won't be working on "how true is it that the load is heavy?". CGS 01:23, 14 Nov 2003 (UTC).

What is this supposed to mean: "Al St.John (1893 - 1963) successfully incorporated the bearded "Fuzzy" in a series of Cowboy B-movies. See also: Westerns."? Is it a caharcter that just has the name "Fuzzy"? Or do the b-weterns by St.John somehow exemplify fuzzy logic? If that is the case the sentence should be rewritten.

I've been adding new fuzzy logic articles: fuzzy associative matrix, Combs method, and most recently defuzzification. I decided to create these in separate pages because they can be treated in depth in their own right, although there is not much depth at these pages yet. - Furrykef 06:31, 3 Oct 2004 (UTC)

Whether or not a statement has a certain determinate truth-value is different from whether or not we are able to know or ascertain the truth-value of a statement. Fuzzy logic is used to deal with vague concepts and predication - it is not an epistemic or doxastic modal logic used for capturing notions like degrees of certainty. Hence the deletion of the section involving the (confusion about the) "controversy" over fuzzy logic. Nortexoid 04:41, 7 Nov 2004 (UTC)

As a statistician it is quite irritating to be told that FL is

"...generally rejected by mathematicians and statisticians because it seems to contradict the

principle of bivalence."

The idea that mathematicians, who invented undecidibility, would reject a form of logic because it involved a form of undecidibility is stupid.

FL is controversial and the critics, like myself, should be acknowledged.

The chief arguments against FL in my view are

a) Exaggerated claims are made for it. The claim that it is a generalisation of set theory is simply false, as membership functions are functions, and functions are defined in terms of sets. Thus FL is built on set theory, and is so not a generalisation of it.

b) FL is used for both deterministic purposes and decision-making under uncertainty. For deterministic purposes it does not offer much of an advantage over simple percentages. For decision-making under uncertainty it should give the same answers as decision theory or there should a good reason why not. It does not give the same answers as decision theory. The reason is that the solutions it provides are, in decision theory terms 'inadmissible' (i.e. non-optimal). FL is simply a 'quick and dirty' ad hoc technique. There is a place for 'quick and dirty' techniques in engineering, as long as one knows that that is what one is using. However, I suspect that many people using FL think they using a rigorous technique.

c) Conventional Popperian philosophy of science lays emphasis on statements which empirically falsifiable. The FL set membership functions are not empirically falsifiable, whereas probability statements (even Bayesian subjective probabilities) are capable of refutation with probability 1 - epsilon, for any positive epsilon. Blaise 19:54, 25 Apr 2005 (UTC)

Well, if you think you can improve the article, by all means do so. Just be sure to keep it NPOV. - furrykef (Talk at me) 20:50, 25 Apr 2005 (UTC)
To add my own opinion, I don't think the implementation of fuzzy logic really accomplishes anything that can't be done with other math. I think where fuzzy logic wins is the way you look at a problem. Sometimes a more linguistic approach is more appropriate, and in my opinion, proper fuzzy logic (as opposed to the way it is often applied) is all about being able to phrase a problem and its solution in linguistic terms. Then the solution becomes obvious, and should be easy to implement.
Also, I've been wanting to speak to an "antifuzzy" person for a long time; now that I've met one, I must ask: why was it that the Sendai Subway was (is?) the smoothest subway ride in the world if its use of fuzzy logic is easily replaced by conventional logic? :) - furrykef (Talk at me) 22:34, 25 Apr 2005 (UTC)

>I think where fuzzy logic wins is the way you look at a problem. Sometimes a more linguistic approach is more appropriate, and in my opinion, proper fuzzy logic (as opposed to the way it is often applied) is all about being able to phrase a problem and its solution in linguistic terms. Then the solution becomes obvious, and should be easy to implement.

I can go along with that.

Blaise 11:37, 28 Apr 2005 (UTC)

>why was it that the Sendai Subway was (is?) the smoothest subway ride in the world if its use of fuzzy logic is easily replaced by conventional logic?

I don't think I've ever been that particular subway but, with respect, I'd remind you of the logical fallacy of 'Post Hoc Ergo Propter Hoc' (literally, 'after therefore because) in which one assumes that because event B follows event A one assumes that event A caused event B. In the 1970s an entire issue of Technometrics was devoted to FL. Peter Cheeseman of NASA Ames wrote some good 'antifuzzy' articles. In one, I seem to remember, he showed how you can take any fuzzy controller and replace it with an equivalent probabilistic controller.

Blaise 11:37, 28 Apr 2005 (UTC)

[edit] Common misconceptions

This section in particular is the most unacceptably POV piece of promotion in an article that reads rather like a sales pitch. I've not got time in the next few weeks to rewrite it, but I'll put the task on my to-do list. ---- Charles Stewart 04:15, 7 Dec 2004 (UTC)

I agree -- and I'm the one who wrote it! It was kind of meant to be a draft, but, as ends up happening too often, I didn't come back to it. I do think it is true that fuzzy logic is misunderstood and this needs to be noted, but a better job needs to be done of it, yes. - furrykef (Talk at me) 20:02, 7 Dec 2004 (UTC)
I think Blaise's revisions handle the issue well now. - furrykef (Talk at me) 01:59, 29 Apr 2005 (UTC)

[edit] This introductory sentence does not make sense.

"Degrees of truth are often confused with probabilities, although they are conceptually distinct, because they need not add up to 100%. "

Totally absent from this sentence is any idea why fuzzy logic might be identified with probability and why they are in actuality different.

A prototype replacement sentence might be: "Degrees of truth are often confused with probabilities: while both deal with "maybes", probability theory deals with the statistical likelihood of the occurrance of an event (hence all probability weightings add up to 100%) whereas degress of truth ..." {fill in the ellipsis at your leisure}.

I'm not an expert in either although I have a fair grounding in probability, so I am reticent to change the article myself. (HTM 2005.04.26 23:50GMT)

For me, fuzzy logic is actually equivalent to probabilistic statements. The basic membership in fuzzy logic, such as 'X being Big' would have some kind of membership function f(x) taking values in [0,1]. Let's say for the moment that this is some kind of triangle with support on [a,b], f(a)=f(b)=0 and f((a+b)/2)=1.

This is exactly equivalent to defining the conditional probability function for X given that X is big i.e. p(x|X_is_big), having the above shape and normalised such that \int p(x|X_is_big) dx = 1

Then you can go on and use standard probability theory and 'fuzzy logic' becomes 'probabilistic inference'. So, what is the advantage in introducing yet another nomenclature? Maybe there is something inherently interesting about fuzzy logic, but it just looks like clumsy probabilities to me. Please correct me if I hold misconceptions, though. --Olethros 23:55, 21 December 2005 (UTC)

The sentence "fuzzy truth represents membership in vaguely defined sets,..." does not make sense. I think the sets are precisely defined, no matter what form they are in, triagular, guassian, etc. If not, how could, for example, Fuzzy Controllers work? --JustAnotherJoe 03:23, 27 December 2005 (UTC)

[edit] Possible bad example of a non-probability truth degree?

With only his little toe in the dining room, we might say Bob is 0.99 "in the kitchen", for instance. No event (like a coin toss) will resolve Bob to being completely "in the kitchen" or "not in the kitchen", as long as he's standing in that doorway.

Wouldn't this 99% degree of truth correspond easily to a probability, namely that the center of a randomly selected particle of Bob's body is within the kitchen? --Damian Yerrick 02:41, 29 Apr 2005 (UTC)

While I don't think that example is particularly good, and your statement is correct, I'd say that example is contrived. Of course nobody would actually think of the problem as, "what percent chance is there of a random particle of Bob's body being within the kitchen"? You could really phrase many if not all statements of fuzzy membership that way. For instance instead of asking if the apple is half-eaten, you might ask, "what percent chance is there of a randomly chosen particle that once made up this apple has passed through somebody's digestive system"? - furrykef (Talk at me) 04:42, 29 Apr 2005 (UTC)

I disagree. This probability-oriented interpretation of fuzzy set membership assumes one particular membership function. Sigmoid fuzzy membership functions, for example, would not fit such an interpretation. -Predictor

I was objecting to that paragraph's implication of a bright line between probability theory and fuzzy logic, a bias toward Dr. Zadeh's point of view and against Dr. Kosko's. Like Dr. Kosko, I see some overlap, and contrived corner cases are useful for pointing out this overlap. Fuzzy metalogic anyone? --Damian Yerrick 17:36, 7 May 2005 (UTC)
A sigmoid fuzzy membership function is a perfectly valid density, though, in the same way as the uniform distribution, P(a < X < b) by itself does not tell you much since it's infinitesimal. On the other hand, you could just write the density p(x) = Z / (1 + exp( − x)), where Z is some normalisation constant, which happens to be the same as that of the uniform distribution. So, if your sigmoid model is the conditional density p(x | C), where C is some category, you can discover the probability that some data X belongs in the category by doing P(C|X) = \frac{p(X|C)P(C)}{p(X)} where P(C) is the prior probability of the category, p(x) is a prior density - note that this must have a support that covers p(x|C), so even if the normalisation constants are infinitely small they will be of the same order of infinity so everything is certainly computable.--Olethros 00:24, 22 December 2005 (UTC)

On a related point, shouldn't it be his big toe? Quite difficult to only enter one's little toe into a room. 81.179.227.183 09:44, 25 July 2006 (UTC)

On the basis that no one's objected, I have changed this :) 81.179.68.182 10:41, 29 August 2006 (UTC)

[edit] Separate from probability

Here is an example that I came up with of how conventional logic differs from FL. It also shows that FL has its niche apart from probability:

Tim and Carl have to unload and clean a truck. Tim is stronger than Carl, and Carl is better at cleaning than Tim. Therefore Tim should unload the truck, and Carl should do the cleaning.

This is a logical approach; we’ve assigned a function to each of the workers and delegated accordingly. But what have we done with Tim’s ability to clean and Carl’s strength? Are they both void? Does Carl have no strength and is Tim a complete slob who is unable to clean anything? It seems that in the process of making a clear cut decision we’ve neglected some abilities. It the industrial and commercial realm, we have failed to use all of our resources. In the above example, we would like to see both workers exercise their greatest abilities, but also be able to utilize the lesser skills they still obtain. This is the foundational concept of Fuzzy Logic; waste can be minimized by reducing the impulse to conclude a black and white solution to a complex problem.

If Tim is stronger than Carl, and Carl is better at cleaning, then Tim should do more of the unloading, and Carl should do more of the cleaning. But both of them should do both tasks.

Now we have a situation where Tim has help carrying the heavy couch, and Carl has someone to help him sweep. Not to mention how much faster both jobs will get done!

If you wanted to place number values on the situation, if Tim is 25% stronger than Carl, then Tim should do 25% more lifting. This is my understanding of FL, unless it is a different logic altogether...

Actually you can't infer anything like that without more information. What if the cleaning is really easy while the unloading is hard work. Then both should spend most of their time unloading the truck... ...unless only one can unload at once etc. 194.237.142.21 14:13, 9 August 2005 (UTC)

A more sophisticated practical example is the use of fuzzy logic in high-performance error correction to improve information reception over a limited-bandwidth communication link affected by data-corrupting noise using turbo codes. The front-end of a decoder produces a likelihood measure for the value intended by the sender (0 or 1) for each bit in the data stream. The likelihood measures might use a scale of 256 values between extremes of "certainly 0" and "certainly 1".

To me this sounds like a textbook example of when to use Bayes' theorem. In other words, it is (should be) an application of probability rather than fuzzy logic. Earlier the article states that

because fuzzy truth represents membership in vaguely defined sets, not likelihood of some event or condition.

and we're definately dealing with the latter in this case. 194.237.142.21 14:13, 9 August 2005 (UTC)

Yeah, I cannot think of a reason why a probability measure over a set does not construe a 'vaguely defined set'.
"If Tim is stronger than Carl, and Carl is better at cleaning, then Tim should do more of the unloading, and Carl should do more of the cleaning. But both of them should do both tasks. ... how much faster both jobs will get done!"
-- As I understand Ricardo's Law / Law of Comparative Advantage, economic theory says that this isn't true at all. Instead, each person should stick to doing whatever he does best, and all the work will get done most efficiently this way. -- 201.78.233.162 02:11, 30 June 2006 (UTC)
But does Ricardo's Law encompass team synergy? In more than a few cases, many hands make light work. If two people can move a piece of furniture more than twice as efficiently than one can, then it maximizes overall efficiency when both people work on it. --Damian Yerrick (☎) 03:25, 5 July 2006 (UTC)

[edit] Proof of DeMorgan's Theorem, excluded middle, Fuzzy Logic

I can't provide a reference, since this is something I figured out myself (although I'm sure others have figured out the same), so I won't add it directly to the article. But as I recall, part of the proof of the DeMorgan's Theorem relies on the law of the excluded middle. Since the excluded middle doesn't exist in Fuzzy Logic, the proof is no longer valid. But you still need DeMorgan's, so it must be adopted implicitly as an axiom. I've never seen anyone else mention this, however.

[edit] "something cannot be 'cold' at N degrees but 'not cold' at N+1 degrees"

Isn't "not-cold at N-1" meant? Somebody confirm this and correct if appropriate.

No, it is saying what is intended, although it may not be saying it well. The point is that in common usage, one would not use a precise cut-off point for "coldness", e.g. saying that 12 degrees is definitely cold, but 13 degrees is definitely not cold. -R. S. Shaw 23:16, 4 December 2005 (UTC)
Somebody else kept changing "cannot" to "can". I really don't understand why this sentence seems to be so hard to understand, considering surrounding context should make it clear, but I finally reworded it... - furrykef (Talk at me) 03:38, 29 December 2006 (UTC)

[edit] Needs a section on logical operations and more

This encyclopedic entry desperately needs mention of the families of ways to represent conjunction, disjunction, negation, and inference. One could also go on to describe the necessary relationships between these using DeMorgan triples. At the moment all this entry has is a brief mention of fuzzy sets. This paucity is then promptly overwhelmed by nay saying.

I would also argue that all the "controversial" labelling should be removed because theoretical paradigms are by definition controversial. That is the Carl Popperian basis of falsifiability. If the paradigm isn't controversial, it's dogma (or incontrovertible fact) and has no place in this discussion. Thus, labelling things "controversial" serves only to advance a personal preference. See also Kosko "claims" to have derived Bay's Theorem. What was the claim? We don't know. The result is incomplete discussions and ignorance.

I would write these myself but I'm busy writing several other papers at the moment. Apologies but its difficult to write something that may be editted by personal preference when for the same effort what I write can be evaluated by a knowledgable editorial review board that already accepts "controversial" presuppositions. I realize this is an excuse so...dare I invoke Schwarzenegger...owl be bock.

[edit] Gianni Bellocchi

I am looking for an expert in the field of fuzzy logic to review the claims on the autobiographical article Gianni Bellocchi. The author (who is also the topic) has made many claims to notability that I am not qualified to evaluate. Thank you. -Harmil 16:08, 24 March 2006 (UTC)

[edit] Applications

This article is pretty good! Some of the other technolgoy articles on Wiki are utter rubbish. Concerning applications - It might be worth mentioning that Fuzzy L is commonly used to control robot navigation and other computer-driven vehicles operating in the real world because of its ability to quickly interpolate logical outputs (for motors and things) with the centre of gravity function. (Also Fuzzy is more and more being used for machine vision algorithms.)

[edit] What is the diffrence between fuzzy logic and binary boolean logic??

Can anyone help?

Basically, fuzzy logic allows a continuous range of truth values instead of just true and false. But as you ask, it really seems that introduction to this article may be a bit confusing for newcomers. Samohyl Jan 20:17, 18 October 2006 (UTC)
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