bill@proxftl.UUCP (T. William Wells) (05/18/88)
In article <1196@bingvaxu.cc.binghamton.edu>, vu0112@bingvaxu.cc.binghamton.edu (Cliff Joslyn) writes: > Furthermore, such a theory exists: Fuzzy Systems Theory. From what I have read in the popular literature, I think that fuzzy system theory cannot work. I wrote a letter to Byte recently in response to an article on fuzzy logic, and so, rather than thinking up another way to say the same thing, I am going to post it here (with some editing). === 4/5/88 Dear Editor: The article "When Facts Get Fuzzy", BYTE, April 1988, p. 285, contains fuzziness of its own: philosophical fuzziness. Take his example of "partly cloudy", which he asserts is ambiguous. As he presents it, it is, but the ambiguity is caused by the fact that "partly cloudy" is not an attribute of the sky but rather of some person's perception of it. A philosophically accurate (at least to a Realist) statement is: "partly cloudy" is the form in which some particular person perceives the sky when the sky contains clouds in certain configurations. People can say "partly cloudy" and be understood by others because the configurations which people see as "partly cloudy" are usually the same. Consider the statement "I see that the sky is partly cloudy." There is no ambiguity there; either I do see this or I do not and the statement is either true or false as a consequence. It might be the case that sometimes, given the same sky, I would report it as partly cloudy or not and one could measure a probability, but that probability is an attribute derived from myself, not from the sky alone. Consider the statement "The sky is partly cloudy." Since this statement omits WHO sees it as partly cloudy, it is ambiguous. One could take a group of people, ask each one whether he sees the sky as partly cloudy, and compute a probability; but that probability is an attribute of groups of people, not of the sky alone. The only way to fix the ambiguity, without making the error of attributing "partly cloudy" to the sky, is to make use of measurements of the density and distribution of clouds in the sky; these being attributes of the sky and independent of who is looking at it. After having done this one can then give a rigorous definition of "partly cloudy" and any statement about the cloudiness of the sky can be validated by using this definition and without reference to who is making it. If, on the other hand, you still would like to be able to say that the sky is X% cloudy and are unwilling to use specified measurements of the sky to do so, how would you proceed? The only way you could do so is by polling people, but of course, as I said, your statistic becomes one about groups of people. The same kind of reasoning applies to the idea of "young". If one specifies WHO thinks that someone is young, the ambiguity goes away; and if one does not, all you can get is a statistic which indicates what fraction of some group of people think that a person is young. Because fuzzy logic is based on a fallacy (the assignment of set membership based on a relationship, while disregarding the thing(s) being related to), any conclusion derived by the use of fuzzy logic is invalid. Cases where it appears to work are sheer dumb luck. I could go on -- but what would be the point? Although the article contains several more philosophical errors, they are irrelevant since the basic premise of the article is flawed. Beware bad philosophy! === So, is my perception of fuzzy systems theory an artifact of my sources, or does it really rest on the philosophic confusion of its proponents?
vu0112@bingvaxu.cc.binghamton.edu (Cliff Joslyn) (05/18/88)
In article <183@proxftl.UUCP> bill@proxftl.UUCP (T. William Wells) writes: >4/5/88 > >Dear Editor: > >The article "When Facts Get Fuzzy", BYTE, April 1988, p. 285, >contains fuzziness of its own: philosophical fuzziness. I saw the article, but only examined it enough to understand that it is very elementary. You object that Fuzzy measures are necessarily subjective, that is, 'partly cloudy' cannot be an attribute of the sky, only of our judgement of the sky. In this case you are right, but what is critical to understand is that it is *also* true of crisp (non-fuzzy measures). For example, I say "What's that smell," you say, "I don't smell anything." Here there is no ambiguity about the smell (it is either there or not), but clearly there is uncertainty as to whether the smell exists or not. Is it *real* uncertainty (maybe it does, maybe it doesn't) or is it this terrible *subjective* uncertainty (maybe I'm wrong, or you're wrong). The truth is that we might never be able to know. This basic epistemic principle is also a natural consequence of moving to a quantum physical model, which incorporates objective uncertainty at its base. >A philosophically accurate (at least to a Realist) statement is: >"partly cloudy" is the form in which some particular person >perceives the sky when the sky contains clouds in certain >configurations. People can say "partly cloudy" and be understood >by others because the configurations which people see as "partly >cloudy" are usually the same. So what? All our theories of nature are built from common observation, and any common observation can be perceived differently by different people, not just ambiguous ones. Does that make it "philosophically inaccurate?" >Consider the statement "I see that the sky is partly cloudy." >There is no ambiguity there; either I do see this or I do not and >the statement is either true or false as a consequence. It might >be the case that sometimes, given the same sky, I would report it >as partly cloudy or not and one could measure a probability, but >that probability is an attribute derived from myself, not from >the sky alone. > >The only way to fix the ambiguity, without making the error of >attributing "partly cloudy" to the sky, is to make use of >measurements of the density and distribution of clouds in the >sky; these being attributes of the sky and independent of who is >looking at it. After having done this one can then give a >rigorous definition of "partly cloudy" and any statement about >the cloudiness of the sky can be validated by using this >definition and without reference to who is making it. You very accurately describe some of the important philosophical problems involved in the determination of fuzzy set membership grades. Your former method is subjective, the latter objective. As I mentioned above, this distinction is useful and necessary: it is critical to know when to act subjectively, when objectively. Frequently we move from one to the other, using one to construct the other. Neither invalidates the other, or is "bad science," or "bad philosophy." >The same kind of reasoning applies to the idea of "young". If >one specifies WHO thinks that someone is young, the ambiguity >goes away; and if one does not, all you can get is a statistic >which indicates what fraction of some group of people think that >a person is young. The real question is whether youthfulness is a natural kind. If so, does it have a crisp definition or not? If not, then it *is* a fuzzy object, no matter how we see it. For example, electrons are natural kinds, but there is a fuzzy boundary between them and the rest of the universe. The position of the particle is ambiguous. This is objective amiguity. On the other hand, the roll of the die is also ambiguous, but is deterministic and chaotic. Here the ambiguity is subjective. >Because fuzzy logic is based on a fallacy (the assignment of set >membership based on a relationship, while disregarding the >thing(s) being related to), any conclusion derived by the use of >fuzzy logic is invalid. Cases where it appears to work are sheer >dumb luck. Is this kind of polemic really necessary? Anyway, your statement appears unsubstantiated, and unrelated to the flow of your previous argument. Please explicate the nature of the fallacy, the 'relationship' alluded to, etc., before denigrating a field you seem to have only a naive familiarity with. -- O----------------------------------------------------------------------> | Cliff Joslyn, Cybernetician at Large | Systems Science, SUNY Binghamton, vu0112@bingvaxu.cc.binghamton.edu V All the world is biscuit shaped. . .
root@cs.qmc.ac.uk (The Superuser) (05/26/88)
<1196@bingvaxu.cc.binghamton.edu> <183@proxftl.UUCP> <1213@bingvaxu.cc.binghamton.edu>, my previous postings Sender: Reply-To: flash@ee.UUCP (Flash Sheridan) Followup-To: Distribution: Organization: EE Dept, Queen Mary College, University of London, UK. Keywords: fuzzy, logic, realism From: flash@ee.qmc.ac.uk (Flash Sheridan) Reply-To: sheridan@nss.cs.ucl.ac.uk or_perhaps_Reply_to: flash@cs.qmc.ac.uk >>Because fuzzy logic is based on a fallacy >Is this kind of polemic really necessary? Yes. The thing the fuzzies try to ignore is that they haven't established that their field has any value whatsoever except a few cases of dumb luck. It _may_ have value, but we must still debate that. From: flash@ee.qmc.ac.uk (Flash Sheridan) Reply-To: sheridan@nss.cs.ucl.ac.uk or_perhaps_Reply_to: flash@cs.qmc.ac.uk
pollock@usfvax2.EDU (Wayne Pollock) (06/01/88)
In article <487@sequent.cs.qmc.ac.uk> root@cs.qmc.ac.uk (The Superuser) writes: >... >>>Because fuzzy logic is based on a fallacy >>Is this kind of polemic really necessary? > >Yes. The thing the fuzzies try to ignore is that they haven't established >that their field has any value whatsoever except a few cases of dumb luck. On the other hand, set theory, which underlies much of current theory, is also based on fallacies; (given the basic premses of set theory one can easily derive their negation). As long as fuzzy logic provides a framework for dicussing various concepts and mathematical ideas, which would be hard to describe in traditional terms, the theory serves a purpose. It will undoubtedly continue to evolve as more people become familar with it--it may even lead some researcher someday to an interesting or useful insight. What more do you want from a mathematical theory? Wayne Pollock (The MAD Scientist) pollock@usfvax2.usf.edu Usenet: ...!{ihnp4, cbatt}!codas!usfvax2!pollock GEnie: W.POLLOCK
nau@frabjous (Dana Nau) (06/02/88)
In article <1073@usfvax2.EDU> pollock@usfvax2.usf.edu.UUCP (Wayne Pollock) writes: >On the other hand, set theory, which underlies much of current theory, is >also based on fallacies; (given the basic premses of set theory one can >easily derive their negation). Not so. Where in the world did you get this idea? Admittedly, _naive_ set theory leads to Russell's paradox--but this was the reason for the development of axiomatic set theories such as Zermelo-Fraenkel set theory (ZF). The consistency of ZF is unproved--but this is a natural consequence of Goedel's incompleteness theorem, and is much different from your contention that set theory is inconsistent. I suggest you read, for example, Shoenfield's _Mathematical_Logic_ (Addison-Wesley, 1967), or Rogers's _Theory_of_Recursive_Functions_and_Effective_Computability_ (McGraw-Hill, 1967). Dana S. Nau ARPA & CSNet: nau@mimsy.umd.edu Computer Sci. Dept., U. of Maryland UUCP: ...!{allegra,uunet}!mimsy!nau College Park, MD 20742 Telephone: (301) 454-7932
jorge@hpfclp.SDE.HP.COM (Jorge Gautier) (06/09/88)
> Sorry, it's a lot more complicated than that. For more details, see my > D.Phil thesis when it exists. When and where will it be available? Jorge
bill@proxftl.UUCP (T. William Wells) (06/19/88)
In article <1073@usfvax2.EDU>, pollock@usfvax2.EDU (Wayne Pollock) writes: > On the other hand, set theory, which underlies much of current theory, is > also based on fallacies; (given the basic premses of set theory one can > easily derive their negation). Just where DID you get that idea? While it was true of the set theory of around a century ago, it is NOT true of set theory today. > As long as fuzzy logic provides a framework > for dicussing various concepts and mathematical ideas, which would be hard > to describe in traditional terms, the theory serves a purpose. You seemed to miss my point: fuzzy systems theory MIGHT be an interesing form of mathematics (but ask a mathematician, don't ask me); BUT in its current form it is not valid as a means of representing the real world.