# Talk:Fuzzy logic/Archive 1

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)

Some of those examples were misleading. So I changed them. I don't think they're ideally placed at the moment, though. There's no need to start discussing the probability theory stuff in the beginning of the article. That should only contain information about what fuzzy logic is! I am not going to bother any more with this article, actually. The possibility theory article is much much better. Perhaps Fuzzy Logic should be just a short article talking about the history of fuzzy logic, etc?? All the controversial stuff is explained very nicely in the possibility theory part. My overall opinion, this article needs to be severely shortened. --Olethros 13:18, 25 May 2007 (UTC)

## 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)

Note this whole argument for and against fuzzy logic is mute and irrelavent. Many decision / classification approaches overlap and in fact can be proven to be the same. Take for instance Tagaki-Sugeno Fuzzy inference. They basically modified the inference system, using fuzzy nomencluture to implement a type of neural network. You can call all of these anything you like, but the names indicate the original motive or application area where this idea cam from. I can even prove some neural networks, baysian networks and fuzzy logic based inference systems are identicle!

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)

## 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)

I agree with the above. The sentence "Degrees of truth are often confused with probabilities, although they are conceptually distinct, because they need not add up to 100%. " is a bit silly, since 'likelihoods', i.e. densities of different things do not necessarily add up to 100%. For example the distribution of heights for men, and the distribution of heights for women. If you take a particular height range, then the numbers of and women won't add up to a constant value obviously. Similarly, for set membership.
A better example: Let's say that we ask people whether they think that a particular temperature is 'hot', 'comfortable' or 'cold'. Then we get three densities for those categories of temperatures. From the three densities you could get the probability that someone will say 'hot' for a particular temperature simply by normalising using the definition of the conditional density (i.e. Bayes formula).
Not only that, but probability theory will also allow you to add prior knowledge as to how probable someone is to say that 20C is hot, if he thinks that 19C is hot. This prior knowledge can be integrated with the data to obtain a posterior more accurate representation of people's perception of temperature. So, in this case, probability seems more general than fuzzy logic. How can fuzzy logic alter set membership based on observations? What would be the meaning of the alteration? What would be the equivalent of prior and posterior/conditional distributions?
Of course, the converse could also be true. Perhaps there is no perfect containment of one construction into the other. However this should be made clear in the article. Any statements claiming more generality of one concept relative to another should be accompanied by a clear counter-example, or a direct reference to one.
--Olethros 08:25, 22 May 2007 (UTC)

## 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, ${\displaystyle P(a by itself does not tell you much since it's infinitesimal. On the other hand, you could just write the density ${\displaystyle p(x)=Z/(1+\exp(-x))}$, 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 ${\displaystyle p(x|C)}$, where C is some category, you can discover the probability that some data X belongs in the category by doing ${\displaystyle P(C|X)={\frac {p(X|C)P(C)}{p(X)}}}$ 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)

## 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)

## 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.

— Preceding unsigned comment added by 65.24.44.155 (talk) 23:03, 2 November 2005 (UTC)

## "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)

## 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.

— Preceding unsigned comment added by 68.42.137.175 (talk) 16:53, 21 March 2006 (UTC)

## 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)

## 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.)

— Preceding unsigned comment added by 130.123.225.69 (talk) 23:21, 11 April 2006 (UTC)

## 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)

The Japanese wikilink to ja:ファジー has been removed twice now. Can anybody explain why? The article there looks relevant to me. It does link to an article about fuzzy sets rather than fuzzy logic proper, but I think that's better than having no link at all, since fuzzy sets are the most important part of the concept of fuzzy logic anyway. - furrykef (Talk at me) 12:50, 24 May 2007 (UTC)

Somebody removed the link again on the grounds that it redirects to the Japanese article on fuzzy sets. I thought about reinstating the link again, but I noticed that it really doesn't discuss fuzzy logic in any broad detail at all. The ideal solution would be to write a Japanese article on fuzzy logic in general, but I don't know enough Japanese to even make a rough stab at it. What should we do? - furrykef (Talk at me) 18:29, 20 June 2007 (UTC)

## Optimal decisions

What is the theory for optimal decision making under uncertainty in fuzzy logic systems? Does one even exist? The classical utility theory integrates just fine with either probabilities or with classical logic. But fuzzy logic?

For example, let's consider some set of possible universes W, composed of the disjoint possibilities w_1, w_2, ..., w_n. Let's say that in all universes you can to things: a_2 or a_2. Let us say that for each universe w there is a known reward funcion R(A;W). If you know that you are in some universe w, then classical logic and utility theory says

If W == w then a = argmax_{a'} R(A=a';W=w).

In fuzzy logic you'd probably have to 'crispify' your membership to decide which universe you are in. Let's call the membership function M(W). Then

w = argmax_{w} M(W=w')

a = argmax_{a'} R(A=a'; W=w).

However, consider the case when there is a w_1, w_2, which both maximise M(.) and for which the following holds:

R(A=a ; W=w_1) = - R(A=a; W=w_2).

In that case, we have no way of choosing an action.

On the other hand, probability theory and utility theory say:

a = argmax_{a} E[R | A=a] = argmax_{a}[sum_w R(A=a';W=w) P(W=w)]

This works because you can marginalise over W to get the expected reward. Again, W is not necessarily 'random', it may just express an uncertain belief. Or it could be both uncertain and random - it depends on how P(W) is defined.

In any case, the question is, how would the choice be made in Fuzzy Logic? It seems that for the actual decision, it'd be something like

If w_1 then a_1

If w_2 then a_2

but the reward does not go anywhere... is something missing here? --Olethros 13:40, 25 May 2007 (UTC)

I'm not sure if I'm smart enough to answer, but here is an attempt. The fuzzy membership function is defined as a whole class of functions. If you pick a particular way of defining it, you can integrate in a similar way to the classical method with that as your measure. An example is using a capacity as your fuzzy measure and integrating with a Choquet integral. I've been meaning to write up some good articles on this stuff, but it hasn't happened yet. I can look up some references if this sounds like the type of answer you want to learn more about, but I'm worried I might be less help than harm. Smmurphy(Talk) 17:03, 25 May 2007 (UTC)
Good, this seems to start making some sense. If you have a capacity v for some set S, you just set S(x)={s|f(s)>x} and integrate.. to get int v(S(x)) dx. Now I can't see how the capacity relates to the fuzzy membership function. If you take any value s in S, then you get the membership fnuction m(s). But the capacity function takes as input sets in S, not single values in S. So, hm.. I would define the capacity as the integral over a subset Q: v(Q) = int_Q m(s) ds. Note that then m(s) would not have to be [0,1] anymore! I think there's a hole here. Probably this is supposed to only work if you set your membership function to be some capacity function.
Which brings me to my problem with this article and with fuzzy logic in general: a lack of good definitions. There apparently many different formalizations of the concept of fuzzy logic. The article needs to reflect the fact that fuzzy logic is only a general concept and nothing precise. First give some idea of what it is like, then write up the list of formalizations. A comparison with probability/whatever makes no sense unless you are speaking about a specific FL sub-field.

--Olethros 18:30, 25 May 2007 (UTC)

## "Perhaps a better question is what technologies do not employ fuzzy logic"

I removed this from the article, at the end of Examples where fuzzy logic is used:

Perhaps a better question is what technologies do not employ fuzzy logic? Most software and mechanical devices and indeed most technologies that work in bounded conditions must, but clearly, since this line will be deleted, this is not popular opinion. Instead of just deleting this line, how about addressing why it's proposition is not accurate?

I can't answer your question because I'm not sure you're trying to say. "Most technologies that work in bounded conditions must?" What do you mean by a "bounded condition", and what makes this statement true?

Also, the line was deleted before not because it was unpopular, but because it was unencyclopedic. It isn't the sort of sentence you're likely to find in an encyclopedia. - furrykef (Talk at me) 15:12, 2 August 2007 (UTC)

Granted it's not appropriate for inclusion in the article but if the same line was posted multiple times this guy probably wants an answer and isn't satisfied with you throwing petty semantics in his face. I think you can answer the question simply by providing an example of a technology that does not in any arguable way utilize fuzzy logic, which would be an appropriate inclusion in the article. Paperflight 02:36, 3 August 2007 (UTC)

## Fuzzy logic - the same as saying quantative logic?

A thought i had triggered by a discussion elsewhere - fuzzy logic relies on a set of defined rules to be determined as being true or false. It relies on creating quantitive measurements of already pre-defined binary states.

An example, a light with a dimmer switch. I've seen people use this as an example of Fuzzy logic, where it becomes a game of defining the state, "where is the light at 50% brightness in relation to 100% brightness" would be the same as saying "For this range of cases tell me where this case = true"? - if, then, else?

In the light example, if you were to look at it further on the cause of it being on at 50% would it not be true enough to say that since electrons are present that the object is in a state of on, and that the 50% is more a measure of the amount of electrons passing through the light resulting in a measurable effect as apposed to a definition of what could be or isnt?

A computer component for example works off 1's and 0's, which is determined by 'how on' a certain object is by the measurable quantity of voltage through it. 0v = off, .5v (or what ever it is) = on, for the states inbetween it is 'unknown', this limitation is set by the designer due to external forces, and if perfect components were to be able to be used as little as 1 electron could be used to define a state, so either the electron is there or it isnt there is no grey, the grey exists cause we choose to define it as a measurable quantive state.

If we are to look at 'experience' as being a modifier for where our value lies in the 'grey' it would be another case of 1's or 0's, you go through the logic, "have i done this before?" yes, 1, the process recalls the information in the objects memory (which is 1's or 0's) and applies it to the current representation of what it has. Binary multiplication, 1's and 0's aside, result - 1 or 0 to proceed. Now i may be over simplifying this, but there is no grey... it either happens or it doesnt.

So to tie it together with another example, a glass full of hot water. We know its hot, our brain interprets the signals sent by our hands to say it is hot. The state of being hot or cold is a binary one. How hot it is per fuzzy logic would indicate that we measure the hotness as a percentage, 0 being stone cold, or 1 being some immesurable heat (for water probably more likely to be 100 degrees where it would no longer be water but vapour). I propose that if the water has temperature from any measurable base state that the value for heat reads as a 1, how hot it is, being a measure of how many times that 1 has been applied to it. Seriphis 09:43, 21 September 2007 (UTC)

Yes. Fuzzy logic is indeed a purely quantitative system and not the qualitative system many seem to assume is its key benefit.

The input condition boundaries are precisely defined using numbers and the output results are also precisely defined using numbers. Once the input and output ranges have been pre-defined then the math used by FL to translate real inputs into real outputs is trivial and deterministic. Every FL system could be replaced by an equivalent numeric lookup map that will give identical results.

FL however does seem a useful way of viewing and mapping some complex algebraic numerical problems as simpler geometric problems and in practical computing terms the use of FL as a high level language could sometimes have undoubted time saving elements in system production.

I believe all the above to be demonstrable and in my own opinion FL is just a novel numerical method rather than the root update in logic that some claim.

Paul J. Weighell 78.146.98.63 (talk) 13:44, 11 December 2007 (UTC)

## Diagram too confusing?

This is regarding the part with the diagram near the top of the article.

In this image, cold, warm, and hot are functions mapping a temperature scale. A point on that scale has three "truth values" — one for each of the three functions. For the particular temperature illustrated with the vertical line, the three truth values could be interpreted as describing the temperature as, say, "fairly cold" (blue arrow), "slightly warm" (yellow arrow), and "not hot" (red arrow).

The "not hot" at the end has been changed to "hot" several times now. This clearly indicates a lack of comprehension of what this is saying. I don't know if it's because they're only skimming the text and not really reading it, or they're reading it but not understanding it. In any case, I wonder if this could be worded better or something to prevent the confusion. - furrykef (Talk at me) 09:33, 30 January 2008 (UTC)

I've made a stab at revising the wording to make it clearer. I only saw two recent changes which deleted the "not", and it's not clear it wasn't the same person each time. Also unclear is whether it was an attempt at correction or simply vandalism. -R. S. Shaw (talk) 05:44, 31 January 2008 (UTC)

It is a combination of lack of comprehension and skimming. I stumbled upon this article and sure enough I just skimmed through until I hit the "Not Hot" and figured it was an error (until I read the article more thoroughly and read this talk page). But, at the same time, it is also a lack of comprehension since I had to read the article several times before fully understanding why it says "not hot". T3hZ10n (talk) 02:58, 13 May 2008 (UTC)

## Examples where fuzzy logic is used

This section does not add to understanding of fuzzy logic. Maybe if explanation was given, otherwise the reader (at least this one) is left thinking "Rice cookers? Huh?" 81.174.226.229 (talk) 12:51, 6 February 2008 (UTC)

## Article quality

This article is not really even start class, for it is chaotic, disorganized and contains errors, unjustified statements and haphazard assertions. Please do not rely on it. I will try to rewrite it over time. History2007 (talk) 11:16, 14 May 2008 (UTC)

## I'm probably talking out my ass, here, but...

I'm relatively sure that:

not A    = 1 - A
A and B  = A*B
A or B   = A - A*B + B
A xor B  = A - 2A*B + B
A nand B = 1 - A*B
A nor B  = A*B - A - B + 1
A xnor B = 2A*B - A - B + 1


Or do I have fuzzy logic mixed up with something else? The article uses min/max for and/or, but that just doesn't seem right to me. —Preceding unsigned comment added by 69.159.9.231 (talk) 20:26, 21 January 2009 (UTC)

Your formulas look like those for probabilities of independent events. Operations in fuzzy logic and probability theory differ, as the degrees they use have different meanings: degree of likelihood in probability theory, degree of membership (or truth) in fuzzy logic. (Admittedly, the meaning of membership degrees is in many areas of fuzzy logic far from clear.) Your operations do occur in fuzzy logic as well, being a very specific selection of logical connectives (in product fuzzy logic with involution - see t-norm fuzzy logics). In general, fuzzy logic uses various sets of truth functions for logical connectives (min and max is by no means the only choice): the most common truth functions for and and or are the so-called t-norms and t-conorms. -- LBehounek (talk) 15:13, 22 January 2009 (UTC)

## 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)
Maybe the name of the section should be changed to something like "Debate over fuzzy logic" Stupidone0 05:48, 31 May 2007 (UTC)
There is no longer a section titled "Common Misconceptions", so I am guessing that this section was renamed "Controversies". I think the "Controversies" section is really a combination of misconceptions and controversies, but all three of the issues in this section are being presented as misconceptions: the heading for each of the three issues says something that is then refuted in the paragraph under the heading. I think that the first subsection, with the heading "Fuzzy logic is the same as imprecise logic" is, in fact, a misconception about fuzzy logic, not a controversy, but the other two issues seem to be legitimate controversies. I think the content of the first subsection should be moved to the introductory section of the article (but without the heading that says "Fuzzy logic is the same as 'imprecise logic'"), to clarify that the "fuzziness" of fuzzy logic refers to the imprecision of some predicates that we use in natural language, not to imprecisions in the system of logic itself. I think the other two subsections should remain in a section titled "Controversies", but their headings should be changed to questions. I think the heading of what is now the second section should be changed to "Is fuzzy logic just a new way of expressing probability?", and the heading of the 3rd section should be changed to "Can fuzzy logic be scaled to larger problems?", or something to that effect. I am new to editing Wikipedia, so I am just suggesting the changes here rather than jumping in and editing it. Dantzu (talk) 05:54, 18 May 2009 (UTC)

## Use in error correcting codes

I would like to put a link to fuzzy logic in the article Soft-in soft-out decoder but I cant find any reliable references. If anyone knows offhand of a good source then please leave it here: http://en.wikipedia.org/wiki/Talk:Soft-in_soft-out_decoder#fuzzy_logic just-emery (talk) 23:52, 2 June 2009 (UTC)

What about Belief propagation? Is there any connection with fuzzy logic? just-emery (talk) 18:18, 3 June 2009 (UTC)

## Difference from probability theory

Maybe I'm being a bit dim, but I still don't quite understand how fuzzy logic differs from a subjectivist view of probability. Does it obey the Kolmogorov axioms? —3mta3 (talk) 19:16, 28 April 2009 (UTC)

No, it does not obey Kolmogorov axioms. In the first place, unlike probability, fuzzy logic is truth-functional: i.e., the value of a compound formula (say, conjunction ${\displaystyle A{\mathbin {\And }}B}$), is a function of the values of the components. For example, in the standard semantics of Łukasiewicz fuzzy logic, the value of ${\displaystyle A{\mathbin {\And }}B}$ is ${\displaystyle \max(1-x+y,0),}$ where ${\displaystyle x}$ is the value of ${\displaystyle A}$ and ${\displaystyle y}$ is the truth value of ${\displaystyle B.}$ That is, the resulting value depends only on the values of ${\displaystyle A}$ and ${\displaystyle B,}$ regardless of which propositions ${\displaystyle A,B}$ are. On the other hand, probability is not truth-functional: the probability of a compound statement (say, conjunction ${\displaystyle A{\mathbin {\And }}B}$ again, which in probability theory is regarded as the intersection of the sets of elementary events representing ${\displaystyle A}$ and ${\displaystyle B}$) is not a function of the probabilities of ${\displaystyle A}$ and ${\displaystyle B}$ (consider the cases when ${\displaystyle A,B}$ are independent and when they are not, which yield different probabilities of ${\displaystyle A{\mathbin {\And }}B,}$ even if the probabilities of ${\displaystyle A,B}$ do not differ between both cases).
Thus, fuzzy logic and (subjective) probability theory describe different phenomena, as they combine propositions in radically different ways. Roughly speaking, probability theory describes uncertainty about sharp results (e.g., "will the die yield 6?"), while fuzzy logic describes unsharp, but certain statements (e.g., the glass is almost full—when we can see how much water is in the glass). Admittedly, it is somewhat clearer (thanks to, e.g., Dutch book arguments) what kind of phenomena probability theory describes than what exactly is described by fuzzy logic. Actually, there is a sort of methodological chaos in the mainstream (i.e., application-oriented) fuzzy logic, and it seems that the traditional fuzzy theory mixes several kinds of phenomena that should be separated (as they obey different laws). Nevertheless, a few narrower branches of what is generally called "fuzzy logic" (e.g., mathematical fuzzy logic or possibility theory) have their basic concepts and the underlying phenomena at least partially clarified. -- LBehounek (talk) 22:40, 29 April 2009 (UTC)
Ok, that makes it a bit clearer. Thanks —3mta3 (talk) 07:51, 30 April 2009 (UTC)
If I pull out a coin that you have never seen before then Bayesian probability theory says that you start with an a priori probability of 50% because there are 2 possibilities (heads and tails). But this is not the actual probability since the coin might be two headed therefore the actual probability is unknown to you. If there is a 10% chance of A happening tomorrow and a 10% chance of B happening tomorrow then what is the probability of A and B happening tomorrow? the answer is of course that the probability is unknown because we dont know whether they are independent or not. but the subjective probability is 1%. In other words it is reasonable of me to expect A and B to happen 1% of the time if I am given NO OTHER INFORMATION. This is not the actual probability itself rather it is something else entirely. It is the subjective a priori probability. just-emery (talk) 01:37, 7 July 2009 (UTC)
Here is a better link to what I am talking about. just-emery (talk) 20:31, 7 July 2009 (UTC)
Bayesian or subjective probability can be thought of as having the same relationship to the actual probability as the actual probability has to the actual outcome. Just as the actual probability doesnt tell us the actual outcome but is useful when the actual outcome is unknown so the subjective probability doesnt tell us the actual probability but is useful when the actual probability is unknown. As such it is a completely distinct concept following completely differert rules. It is completely true that regular probabilities cant be modeled using fuzzy logic but subjective probabilities can be. just-emery (talk) 23:43, 7 July 2009 (UTC)
Again, the rules aren't "completely different" (if not, then what specifically is different?). If an "actual probability" exists then it implies an underlying random process. This is certainly the case for your dice example, for instance. Also, I think you're conflating non-random processes with not knowing the prior distribution, and therefore making estimates of it. Oli Filth(talk|contribs) 23:55, 7 July 2009 (UTC)
What specifically is different? Exactly what I said up above about the 10% chances. The probability is unknown but the subjective probability is 1%. Thats totally different. I get the impression that you dont actually read what I write. just-emery (talk) 00:08, 8 July 2009 (UTC)
Once you've assumed a prior probability distribution, everything follows from Bayes theorem as if it were the actual probability. No rules have changed. Oli Filth(talk|contribs) 08:12, 8 July 2009 (UTC)

## Prod of fractal logic

I'm posting the prod notice here, since this is the most relevant article to the contents there. Fractal logic was proposed by Pescher as a two-dimensional generalisation of fuzzy logic:

A proposed deletion template has been added to the article Fractal logic, suggesting that it be deleted according to the proposed deletion process because of the following concern:
Notability: subject seems to be supported by single, low impact publication that has apparently not been followed up, namely Pescher, 2000 Fractal Logics versus Fuzzy Logics. Google Scholar has mentions a citation in a PhD dissertation, but it is cited in a sweeping way, without use of the content. New publications on the topic would, of course, change the case for notability.
All contributions are appreciated, but this article may not satisfy Wikipedia's criteria for inclusion, and the deletion notice should explain why (see also "What Wikipedia is not" and Wikipedia's deletion policy). You may prevent the proposed deletion by removing the {{dated prod}} notice, but please explain why you disagree with the proposed deletion in your edit summary or on its talk page.
Please consider improving the article to address the issues raised because, even though removing the deletion notice will prevent deletion through the proposed deletion process, the article may still be deleted if it matches any of the speedy deletion criteria or it can be sent to Articles for Deletion, where it may be deleted if consensus to delete is reached.

If you've heard of the subject and think it's notable, please deprod, and make the article there a bit less useless. — Charles Stewart (talk) 09:34, 29 June 2009 (UTC)

## Section removals

I've removed several sections from this article. I wouldn't normally make such a radical move, but the writing in the uprooted sections was either incomprehensible (using notation and terms not introduced properly or at all) or inappropriate in tone (one part even used the first person), or both. If I can, I'll look over the sections I removed at a later date and salvage what I can, but it struck me as best to remove first and examine later, given the numerousness of the content's problems. —Anonymous DissidentTalk 15:20, 29 September 2009 (UTC)

## Objections is POV

The objections section, while informative, is explained from the point-of-view of the fuzzy-logic adherent, and does little to even explain the reasons behind objections before trying to refute them. I'm not particularly concerned with right or wrong here; I'd just like better insight into the issues. 70.250.179.253 (talk) 20:20, 13 March 2010 (UTC)

## Dice example

What does this newly added example have to do with fuzzy logic? It's simply implying an application of Bayesian inference to estimate the a priori distribution, i.e. probability theory - precisely the opposite of what the previous paragraph describes. Oli Filth(talk|contribs) 19:40, 7 July 2009 (UTC)

the previous paragraph shows that fuzzy logic values are not the same as probabilities. the new paragraph shows that fuzzy logic values can be used to express subjective a priori probabilities which are completely different. The previous paragraph was about probabilities not a priori probabilities. A priori probabilities follow different rules than probabilities. See 'Difference from probability theory' where there is already a discussion on this. Just as there are degrees of hot and cold so there are degrees of expecting something to happen.just-emery (talk) 20:40, 7 July 2009 (UTC)

It doesn't show that, it simply states that, with an example that doesn't demonstrate any such application of fuzzy logic! What's more, it would seemingly contradict the original paragraph, on the basis that "prior probabilities are completely different". Why? Oli Filth(talk|contribs) 20:43, 7 July 2009 (UTC)
The first paragraph doest even mention a priori probabilities so how could it contradict it?. The discussion above (difference from probability theory) explains why fuzzy logic works for a priori probabilities. just-emery (talk) 20:52, 7 July 2009 (UTC)
Prior probability is still probability (it's still a distribution in an event space, you just don't necessarily know it). And I've reread the "Difference from probability" thread carefully, and I still can't see where you think it explains the connection. Please point out the relevant part where any parallel between fuzzy logic and Bayes theorem is shown. Oli Filth(talk|contribs) 21:04, 7 July 2009 (UTC)
And you never will no matter how clearly I prove it to you. None is so blind as he who will not see. I am not going to play your 'jump through the hoops' game. Go buy a dog. I am waiting to see what others have to say. just-emery (talk) 00:19, 8 July 2009 (UTC)
Once again (and this seems to be the latest in a series of WP articles where you've been doing this), you haven't proved anything, you've simply asserted something or speculated on something, and seem unable to justify the assertion. It's not up to me prove that it's nonsense, it's up to you prove that the material you added to an article isn't nonsense (see e.g. WP:BURDEN).
I'll repeat the salient point: How, specifically, is fuzzy logic used to model your example of dice? And how, specifically, would the resulting approach be different than a standard probabilistic approach? Oli Filth(talk|contribs) 08:20, 8 July 2009 (UTC)

I'm sorry, but your latest edit is just total nonsense! I'm going to remove the whole paragraph, because not only is it founded in speculative nonsense, but it still doesn't justify, let alone provide a source for. how your examples (which you've posed in a probabilistic framework) are in any way related to fuzzy logic. Oli Filth(talk|contribs) 23:21, 7 July 2009 (UTC)

Fuzzy logic is just multi-valued logic where one does not use all of the possibilities, thus making it easier to model and comprehend. In base 2 (Boolean) logic there are sixteen values to represent the truth tables for two values (2^2^2), but in base five there are 5^5^5 possible connectives, which makes for an unweildy set. However, as the article says it is very possible that one is not using the correct operators for their particular problem. —Preceding unsigned comment added by 75.84.120.95 (talk) 04:41, 6 June 2010 (UTC)

## "Application areas" section

Without any sort of context, the "application areas" section is almost completely devoid of purpose. In what way do rice cookers, dishwashers and elevators use fuzzy logic? At a minimum, references would be useful. Oli Filth(talk|contribs) 22:11, 7 July 2009 (UTC)

Rice Cookers : Utilize fuzzy logic to adapt to environment specific changes in temperature, due to the several distinct phases required (i.e. Boiling, Simmering, Resting, Warming)
Dishwashers : To reduce water consumption, to guage particulate emission in the wastewater, etc.
Elevators : Traffic rate estimation, multiple floor calls, sequence of call optimization, etc.
The list goes on and on...Google is your friend. Whompy40 (talk) 15:25, 21 June 2010 (UTC)

## Logic Values

The first paragraph discusses logical variables that are neither 1 nor 0. From my long-time-ago memory of this at school, I thought Boolean algebra dealt with values that are either TRUE or FALSE, and not integers at all. Using one and zero is merely the implementation computers need to use, isn't it? Rojomoke (talk) 14:55, 30 June 2009 (UTC)

George Boole originally used 0 and 1 for false and true respectively, c.f., the Burris ref from The Laws of Thought. — Charles Stewart (talk) 15:02, 30 June 2009 (UTC)
There is a subset of mathematical Logic named "Boolean Algebra". It does exactly what you say it does and exists a lot longer than Fuzzy Logic but I have not met anyone promoting Fuzzy Logic who seems to be aware of its existence. I think Boolean algebras should definitly be mentioned but I am not sure how since I see no difference between them and Fuzzy logic. T3kcit (talk) 15:50, 13 August 2010 (UTC)

## Article quality

The article quality is in the mid-low level. The article is not "junk" as such, but is full of incorrect, semi-correct and unsupported sentences all over. For instance, it does mention possibility theory, as it should, but does not do it justice at all. I will try to do some minor clean up, but a total rewrite would even be better.

Some obvious and at times laughable issues are:

• The article has hardly even defined what the topic is, but gives space to "decidability issues"! Hello? That is just a crazy method of topic selection. Another example is fuzzy relational databases, of which none is in use in the world today.
• Basic ideas such as linguistic variables etc. are discussed, but poorly.
• I cleaned up section names such as "mahematical fuzzy logic" that just sounded less than informed, but that trend is present throughtout.

A rewrite is really needed. History2007 (talk) 12:14, 5 April 2010 (UTC)

## Mentioning of Probabilistic Methods

As History2007 mentioned before, I think that probability theory is not done justice in this article. Not only is it mentioned to short, but also wrongly. Whoever wrote this does not understand probability theory at all. It is long established in mathematics that probabilities do not only processes (like throwing a dice) but also uncertainty.

I would think that every user of probabilistic methods would see the "hot" "warm" "cold" example in the article as a perfect fit for a probabilistic model. Since I do not understand how fuzzy logic is different from probabilistic methods here I can not correct the article. But I would remove this description of probabilistic methods that is quite wronge if no one can change it. T3kcit (talk) 15:56, 13 August 2010 (UTC)

## Fuzzy vs. Vague

While I have great respect for Lotfi Zadeh's contributions to this field of inquiry, and recognize that his seminal 1965 paper may well be the first publication to use the term "fuzzy set," it seems to me that the original proposal for this approach was made by Max Black in 1937: "Vagueness - An exercise in logical analysis" Philosophy of Science, 4:427-55, October 1937, motivated, in part, by earlier comments by Bertrand Russell and Henry James. Note, in particular, Appendix I (op. cit.) Not being an expert (or even a professional!) in this field, I will leave it to others to review this early proposal and incorporate, at the least, a note, in the article on Fuzzy Logic.

I think many people could be considered to have written about vagueness, going perhaps as far back as Augustine of Hippo, but that debate is probably beside the point in an article with so many other problems. History2007 (talk) 21:04, 5 September 2010 (UTC)
Comment: The Max Black paper cited above can be found on JSTOR at http://www.jstor.org/pss/184414 . This syllabus for a course on vagueness is also interesting: http://www.columbia.edu/~av72/Vagueness/Syllabus.pdf -- 79.123.75.59 (talk) 07:39, 29 October 2010 (UTC)

## Simple example of fuzzy logic showing its connection to regular deductive logic

Deduction Fuzzy logic

I know Aristotle is a man.
I know all men are vain.
Therefore I know Aristotle is vain.

I think Aristotle is a man.
I think all men are vain.
Therefore I expect that Aristotle is vain.

just-emery (talk) 01:07, 30 October 2010 (UTC)

Actually, shouldn't the last one be...
Fuzzy logic

Aristotle is a man to some degree.
All men are vain to some degree.
Therefore Aristotle is vain to some degree.

Jcmorris-mts (talk) 02:18, 21 January 2011 (UTC)
Exactly. Despite the aim of fuzzy logic in broad sense (as claimed repeatedly by Zadeh and others) of capturing the figures of reasoning like those cited above, it is clear that truth-functional [0,1]-valued fuzzy logic is only capable of formalizing arguments like the one you give. Such modalities as "I know", "I think", or "I expect" belong to other branches of logic (epistemic, doxastic, or probabilistic), and although they can be fruitfully combined with fuzzy logic (to yield corresponding fuzzy modalities), the basic apparatus of fuzzy logic described in the article is restricted to arguments involving graded truth rather than other modalities. Therefore I'd oppose including the above examples in the article (which should anyway be completely rewritten, as it contains several disputable claims and does not represent the field adequately). -- LBehounek (talk) 15:01, 26 January 2011 (UTC)

## Distinction from other logics

While the distinction with boolean logic is obvious, the distinction with other logics, especially those who allow values in the range [0,1] is unclear.

For example, there is a probability derived for of logic using values in the range [0,1], where NOT(x)=1-x, AND(X,Y)=X*Y, and OR(X,Y)=1-((1-x)*(1-y)). That would be the exact interpretation traditional logic gates in a probability setting, as long as all variables in independent. It also gives an acceptable approximation in the event that the random variables have only a small correlation.

There is also the standard probability formulas like Bayes' Theorem, Law of total probability etc.

But Fuzzy Logic appears to not be probability based. Rather than 0.5 meaning 50% chance of being 1, and 50% chance of being 0, it means a 100% chance of being 0.5.

Hmm... the implications of this is unclear. This article could really use a re-write with a more realistic example, and a whole section explaining how it differs from other things. It looks like it is intended to be used as part of a control system.

... 76.243.42.111 (talk) 17:35, 30 October 2010 (UTC)

## Germanized Use of Abbreviation "resp." (an en.wiki-wide issue, but relevant here)

This is, I'm pretty sure, a serious problem on Wikipedia — one which, of all things, can cause a sort of logical confusion! — and kind of tough to search out (since someone once decided that punctuation need not be searched). There is a German abbreviation, bzw., for beziehungsweise, which can mean "respectively", but more often is used in the senses "and accordingly", "as the case may be", and especially common in parentheses, "or" / "or rather". In this article, as of this present posting (and in many others on Wikipedia -- though I am raising the issue here, for the first and perhaps only time...), the common abbreviation for English "respectively" – resp. – is being used, in parentheses at it happens, as if it meant "or" / "as opposed to", which it most emphatically cannot do in English. As some editors (presumably German-speaking?) may, I understand, quite honestly not have realized, respectively in English is much more restricted in meaning and application than beziehungsweise, as I will now spell out for any editor who may have been assuming the two were broadly equivalent.

In the section entitled Predicate fuzzy logics, where the following is written:

...the infimum (resp. supremum) of the truth degrees...

...what is intended by resp. (an over-broad translation, a mistranslation in this context, of German bzw.) is something like "as opposed to", or even simply just "or". This is of course not at all what is meant by English resp. / respectively, as in Pat and Chris are married to Jan and Lynn, respectively or even (with a syntax closer to that of beziehungsweise) Pat and Chris are married respectively to Jan and Lynn. The intent of both of these sentences is that the first individual named is married to the third individual, and the second one is married to the fourth. Pat and Chris are not a married couple, nor are Jan and Lynn. (Bear with me please; most native English speakers will know this, but some of our German speakers I believe do not.) A construction like *the infimum respectively the supremum, lacking two or more pairs, is not only ungrammatical, but is meaningless. –Not what you thought, German-speaking friends? Well, no great harm, no foul, but please do spread the word: So far as I can tell, this odd cross-linguistic phenomenon is widespread on English Wikipedia.

Note, I'm going to leave this evident error as it stands for now, because there is a broader issue: It's my hope that the subcommunity of our editors who are propagating it across the en.wikepedia subdomain will tend to it, both here and everywhere else where it may be, as I am certain it is here, a problem. (Thanks for everybody's patience under the onslaught of all this detail.) IfYouDoIfYouDon't (talk) 17:21, 9 March 2011 (UTC)

## Article needs a crticism section

See [1] for instance. Tijfo098 (talk) 17:49, 13 April 2011 (UTC)

Vandalism ? there are multiple occurrence as Luzzy Fogic. —Preceding unsigned comment added by 202.184.111.67 (talk) 14:28, 22 April 2011 (UTC)

## Japan's Fuzzy Boom

Japan went through a "Fuzzy Boom" in the 1980's. All sorts of devices (like vacuum cleaners, etc) were claimed to incorporate fuzzy logic in their programming. It might be nice to include this in the article. --Westwind273 (talk) 19:29, 12 September 2011 (UTC)

## Ignorance, huh?

(last word of 2nd or 3rd segment) Well I like the way that sounds but no sources are cited so until then this sounds like this might be a case of subjective bias. Prove me wrong! I want to read the article. — Preceding unsigned comment added by Ddd1600 (talkcontribs) 00:55, 4 December 2011 (UTC)

## Not that good

The first sentence states "The reasoning in fuzzy logic is similar to human reasoning". I think this is to be a bit too optimistic. — Preceding unsigned comment added by 37.2.234.168 (talk) 21:47, 8 July 2012 (UTC)

## Fuzzy is not probabilities, is not for uncertainty

The article makes several erroneous claims. It first says that fuzzy logic is a form of probabilistic logic. It is not! For one thing, fuzzy logic is truth functional, while probabilities are not. It is also claimed that fuzzy is a way to deal with uncertainty. It is not! Fuzziness is used to describe _imprecise_ notions (like hot, or tall), not uncertain notions. — Preceding unsigned comment added by 141.76.75.36 (talk) 11:21, 3 August 2012 (UTC)

'unsigned' makes an important point. Fuzzy logic would be useless for any real world application if it dealt with probabilities. In a control system, you have exact numeric input values (called "crisp" by Zadeh), and you produce exact numeric (crisp) output values. There is NO uncertainty.

The real value of fuzzy logic, not mentioned in the article, is this: Fuzzy logic control systems DO NOT require a mathematical model of the system. They easily control complex systems where mathematical modeling is impractical, and, if properly constructed, do it extremely well.

Engineers worldwide are quietly using fuzzy logic in control applications, because they know it works. Leave it to the mathematicians to argue and criticise. — Preceding unsigned comment added by 99.140.183.155 (talk) 00:47, 10 March 2013 (UTC)

## This is a controversial discipline - so why is word "criticism" not found in the article?

fuzzy logic has the dubious distinction of having a whole lot of mathematicians and programmers saying that it is the wrong way to do things, as opposed to other AI techniques. This is easily confirmed using (fuzzy logic criticism) google search. So how come this article contains no criticism whatsoever? 76.119.30.87 (talk) 15:13, 15 May 2012 (UTC)

I can't really find anything... 80.111.56.106 (talk) 23:17, 24 April 2013 (UTC)

## Fuzzy Logic is inconsistent

According to the article, any truth values between 0 and 1 can be assigned to sets. But this is wrong: The axioms only admit the truth values truth(0) and truth(1). Proof: Let 0 denote the empty set, 1 the universe. Then for any x Max( truth(x), truth(not x) ) = truth(1) Min( truth(x), thruth(not x) ) = truth(0)

Therefore truth(x) equals either truth(0) or truth(1), for any x.

q.e.d.

Therefore, applications of fuzzy logic assigning more than two different values are inconsistent. I think, fuzzy logic should be deprecated. Hans-Rudolf Thomann (mathematician)HRThomann (talk) 07:37, 21 August 2012 (UTC)

I think you're missing the point of fuzzy logic. 80.111.56.106 (talk) 23:30, 24 April 2013 (UTC)

## The story is lost?

I was taught this was based on a hypothetical Artificial Intelligence question of whether a bear is fuzzy. Suppose it is a very fuzzy bear (with high density of hair) and you pluck one hair from the bear. Is it still fuzzy? Because the bear's hairs are finite in number, repeating the process would eventually yield a bald bear, which is not at all fuzzy. What was the transition point, at which hair # or % or whatever? I forget who posed the question in some paper.

I presume one can ignore the dangers of plucking hairs from bears. That's the sort of job grad students are for.

Michael McGinnis (talk) 20:19, 9 July 2013 (UTC)

Either the author of this wiki article and the authors of "Importance of Fuzzy logic in Multiple Powers Genera ting Area over PID" are the same or somebody copied big parts without citation, e.g., "Both degrees of truth and probabilities range betwe en 0 and 1 and hence may seem similar at first. For example, let a 100 ml glass contain 30 ml of water. Then we may consider two concepts: Empty and Full. The meaning of each of them can be represented by a certain fuzzy set. Then one might define the glass as being 0.7 empty and 0.3 full. Note that the concept of emptiness would be subjective and thus would depend on the observer or designer. Another designe r might equally well design a set membership functi on where the glass would be considered full for all va lues down to 50 ml. It is essential to realize that fuzzy logic uses truth degrees as a mathematical model of the vagueness phenomenon while probability is a mathematical model of ignorance." ("in Importance of Fuzzy logic in Multiple Powers Generating Area over PID", Suresh Chand and Vinod Kumar Singh, p 351, http://www.jecet.org/issues/volume2/issue2/JV2II_18.pdf) --202.79.203.59 (talk) 07:54, 30 September 2013 (UTC)

The referenced paper (at http://www.jecet.org/issues/volume2/issue2/JV2II_18.pdf) was submitted 4 April 2013. The quoted part clearly came from Wikipedia, where the basic text of that passage first went in at 13:12, 25 May 2007. The referenced paper in fact substantially duplicates what is in this article (which was developed by many people over the years). The paper's title doesn't make sense, nor are the themes mentioned in it discussed in the abstract or body. Most likely the paper is a joke. --R. S. Shaw (talk) 06:58, 2 October 2013 (UTC)

## Does this make sense?

Does this: 'It is an open question to give supports for a Church thesis for fuzzy mathematics the proposed notion of recursive enumerability for fuzzy subsets is the adequate one.' make sense? (From the section Decidability issues for fuzzy logic.)— Preceding unsigned comment added by 86.145.58.111 (talk) 14:24, 14 November 2013 (UTC)

## Fuzzjective

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Genezistan (talk) 05:44, 19 August 2013 (UTC)

I don't mean to sound impolite, but what on earth does all that mean? 86.145.58.111 (talk) 14:29, 14 November 2013 (UTC)