Talk:Fuzzy set

message: Perhaps a section about software implementation of theories could help I say this after finding in some other pages a section named like that.
I've created my own via R with BaseSet but I'm hesitant to add it myself.
Dròpol (talk) 09:52, 1 June 2022 (UTC)
replies: text: there have been lots in engineering, almost invariably piece-wise linear controllers. apparently engineers (1) cannot get their heads around non-linear dynamics (an unfortunate consequence of the fact that they are taught that calculus is something that happens "in the frequency domain") and (2) they must really like the term fuzzy, which sounds like cutting edge maths, as opposed to gluing PIDSs together in messy ways 2A01:CB0C:CD:D800:D1B7:91BB:C98D:C0FC (talk) 08:19, 19 December 2022 (UTC)
thread_title:  Implementations? 

message: Citing from the article:
A fuzzy set is a pair (A, m) where A is a set and m : A \rightarrow [0,1]. 
For each x\in A, m(x) is called the grade of membership of x in (A,m).
If m is defined on A (i.e. takes as input all of the members of A) then it will never return 0. Accordingly,
"Let x \in A. Then x is called not included in the fuzzy set" does not make much sense, as does
"The set \{x\in A\mid m(x)>0\} is called the support of (A,m)" (seeing that m(x) > 0 for every x in A).
A counter-argument would be to say that every element is contained in A. Seeing that this leads to there only being exactly one set, encompassing everything, this does not seem to be a good idea. If posing the question whether this set would contain itself, we arrive at the fuzzy equivalent to Russel's Paradox. Illuminations showing that I am mistaken are, of course, very welcome. — Preceding unsigned comment added by 195.169.201.86 (talk) 20:20, 10 March 2012 (UTC)
replies: text: By the definition of a function, m\colon A\rightarrow[0,1] can of course assign 0 to some (or even all) elements of A. In other words, m(x)=0 is a legitimate value of m for x\in A. -- LBehounek (talk) 09:45, 12 March 2012 (UTC)
replies: text:  I am aware of the fact that [0,1] is the codomain of m. Yet: The definition states that we talk about the fuzzy set A. The membership function is defined on the members of A (= has the type A -> [0,1]). As such, we can only give it arguments which already belong to A, x \in A. As such, for every x this function will yield a value > 0 (because it tests for membership and we only supply members). I think a solution would be to define the membership function on a universe U containing all of the objects (even those not in the fuzzy set) and then define the membership function for a fuzzy set A on this universe instead. So its type would be U->[0,1]. It would then actually return 0 for elements which are in the universe, but are not in the fuzzy set. See also the article "Fuzzy models—What are they, and why?[Editorial]", JC Bezdek - Fuzzy Systems, IEEE Transactions on, 1993  — Preceding unsigned comment added by 195.169.201.86 (talk) 11:59, 13 March 2012 (UTC)
replies: text:  In the article, A is not the fuzzy set, but the domain of the fuzzy set (a crisp set, the universe which you call U in your reply). The fuzzy set is the pair (A, m), where m is a function from the crisp universe A to [0, 1]. The confusion may be caused by the fact that fuzzy sets (or their membership functions) are often denoted by A, B, etc. in the literature, while the universe is more usually denoted by U or X. Perhaps changing the notation in the article from A to U would prevent the confusion: I'll make the change right now. -- LBehounek (talk) 15:48, 14 March 2012 (UTC)

text: Yes, Gottwald's two-part survey paper is good. I found it myself while browsing his list of publications. I'll add it to the further reading section, now that we have that. Tijfo098 (talk) 16:44, 13 April 2011 (UTC)

text: The first one concerns fuzzy sets, saying that axiomatic fuzzy set theories exist which do not rely on non-fuzzy set theories (as has been shown at your request.) Oh my, how clever! A side by side comparison of the axiom lists quickly reveals how the rabbit is magicked out of the hat - it will even show you how the rabbit got there in the first place. 2A01:CB0C:CD:D800:D1B7:91BB:C98D:C0FC (talk) 08:22, 19 December 2022 (UTC)
thread_title:  Some topics 

message: I notice that there is no definition of \subseteq or \cup etc. w.r.t. a fuzzy sets.  Someone should add these and other important fuzzy set operators to this article!InformationSpace 06:00, 4 May 2007 (UTC)
thread_title: <math>\subseteq, \cup</math> 

message: I just ran across this article on new pages patrole, but I'm way to unexperienced in this field to get any proper sources or better content for the article. It seems related to fuzzy sets though (the mathematics applied to fuzzy sets?). I posted an expert tag there, but maybe some of the editors of this page have a better idea what to do with it. (maybe a redirect? maybe a reverse redirect? keeping the article as a seperate one with seperate content?) Thanks. Martijn Hoekstra 21:54, 4 November 2007 (UTC)
replies: text: you're also no great shakes at spelling English words, but anyway, if you are a decent mathematician it is not surprising you know little about the fuzzy business. It does not do anything that advanced maths does not already do better, but it is the darling of engineers, economists and sundry 3rd rate riff raff . 2A01:CB0C:CD:D800:D1B7:91BB:C98D:C0FC (talk) 08:25, 19 December 2022 (UTC)
thread_title:  [[Fuzzy Mathematics]] 

message: What is "an uncertain set"?  yoyo (talk) 05:46, 5 October 2009 (UTC)
thread_title:  An uncertain set 

message: The original paper of (Von) Dieter Klaua doesn't seem to be online. A later (1966) paper by him is though . Klaua lived in East Germany. Tijfo098 (talk) 16:18, 13 April 2011 (UTC)
thread_title:  Klaua 

message: What are the implications of fuzzy sets? Is there any practical application of this subject? 78.86.61.94 (talk) 23:32, 17 April 2013 (UTC)
replies: text: well, there have been lots in engineering, almost invariably piece-wise linear controllers. apparently engineers (1) cannot get their heads around non-linear dynamics (an unfortunate consequence of the fact that they are taught that calculus is something that happens "in the frequency domain") and (2) they must really like the term fuzzy, which makes to sound like cutting edge maths, as opposed to gluing PIDSs together in messy ways. On a less frivolous note, no, the subject does not afford any advantage or insight beyond poor mathematicians playing around endlessly with definitions. Especially egregious are claims that quantum mechanics makes more sense from a fuzzy point of view --- that amounts to pointing students in a direction diametrically opposed to the truth. 2A01:CB0C:CD:D800:D1B7:91BB:C98D:C0FC (talk) 08:28, 19 December 2022 (UTC)
thread_title:  Implications 

message: Please somebody remove the intruding material on Baoding Liu's credibility.  — Preceding unsigned comment added by 93.156.32.168 (talk) 18:27, 16 March 2014 (UTC)
replies: text: You are probably right. It is just being dumped here. I will just leave the entropy material there.  SaundersLane (talk) 19:29, 2 November 2015 (UTC)
thread_title:  Plea 

message: Is it just me or does the whole concept of fuzzy logic complete quackery? Isn't the entire assumption of this that there is definitively a right way and wrong way to do something in the universe.  The universe meaning absolutely everything. Isn't kind of an obvious truth that reality is in the individual context not the everything ONE? If I call one person tall and you call that same person short. That doesn't mean there is a value between 1 and 0. It means that the value for me is 1 and the value for you is 0(or vice versa).  I think cognitive science has to trump this. If you don't question fuzzy logic's legitimacy maybe you should read "The Psychology of Human-Computer Interaction" or better yet Unified Theories of Cognition by Allen Newell that outlines an architecture called SOAR. His work is much more consistent and universal than this fuzziness and actually has had profound practical applications for decades. Its basis is contradictory to the foundation of this page's subject matter. Fuzzy logic is just that...logic.  Logically consistent does not mean it has truth beyond that in actual reality. I am even willing to call fuzzy logic a brilliant idea, but it should be written as pseudo math, not real math.
Also, why the heck is "fuzzy electronics" considered a branch of electronics? This is absurd!
: Well, fuzzy logic seems to appeal to people who do not seem to know what you can do with measure theory, or, for that matter, curves that aren's straight lines.2A01:CB0C:CD:D800:D1B7:91BB:C98D:C0FC (talk) 08:30, 19 December 2022 (UTC)
thread_title:  Vortex-Based Mathematics of Set Theory? 

message: What is Cr in the definition of fuzzy entropy?
Moreover, "a fuzzy variable with continuous membership function" is the same thing as a continuous function from ℝ to [0,1]?
:Using Cr is another notation not defined here. See Xiang Li: Fuzzy cross-entropy, PDF. However there is an equal sign inside the Argument of Cr, not a greater-or-equal and I doubt if the latter is correct as it is given here. Cr { A=t } may appear to be the correct notation. --Moyalingde (talk) 23:14, 3 December 2017 (UTC)
thread_title:  Entropy 

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