Re: Fuzziness as opposed to Probability

From: Robert Ehrlich (bobehrlich@home.com)
Date: Mon Aug 13 2001 - 22:34:31 MET DST

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    I am an applied person who uses statistical methods to provide criteria for
    making decisions that may involve a lot of money and their success will be
    apparent in short order. IMHO neither fuzzy logic, frequentist approaches, nor
    Bayesian approaches ever "prove" anything. They at best raise points that must
    be included in a decision making process. They are most useful when they
    provide"non common sense" results because it forces us to carefully reconsider
    our understanding of the underlying system. "it is good because it works"
    strikes me as a circular argument unless there is a real world penalty for being
    wrong. If you are looking for places to drill a 5 megabuck oil well or trying
    to decide whether an occasional death is worth using a new drug things get sober
    quickly and no one says that a numerical result by itself
    "works". Success is not a good criterion if there is no significant penalty for
    being wrong. Banging on pots always keeps the sun from being eaten by the moon
    during eclipses. it "works" so what?

    Herman Rubin wrote:

    > In article <3B69F78D.6020407@bellatlantic.net>,
    > <predictr@bellatlantic.net> wrote:
    > >Radford Neal wrote:
    > >"The whole point of constructing a mathematical formalism for inference
    > >is to produce conclusions or decisions that are more reliable than would
    > >be produced by unaided human intuition."
    >
    > >Will Dwinnell responded:
    > >"To me, this is the crux of the matter. I don't know about the fine
    > >point that this statement was in reference to, but I think it expresses
    > >quite well what I think of as the "engineer's perspective".
    >
    > ..................
    >
    > >My general question to critics of fuzzy logic in general is: what is
    > >wrong with using fuzzy logic if it provides useful results?
    >
    > ..................
    >
    > >Herman Rubin asked:
    > >"Tell me how to get results."
    >
    > >I am not sure what you are asking. The construction of fuzzy logic
    > >systems is well-described in the literature and I'd refer you to Earl
    > >Cox's "The Fuzzy Systems Handbook", but I suspect you're asking about
    > >somthing else?
    >
    > >Herman Rubin continues:
    > >"How does fuzzy logic contribute to getting a consistent scheme of action?
    >
    > >Can you elaborate on what you mean by a "consistent scheme of action"?
    >
    > >Herman Rubin continues:
    > >"Expectation derived from probability does this. Consistent action has
    > >been shown to force probability."
    >
    > The point is to come up with a procedure for preferences
    > between actions, so they are not contradictory, and put
    > this on a quantitative basis so as to go from simple
    > situations to complicated ones.
    >
    > >Herman Rubin, in another message wrote:
    > >"Complete a "fuzzy" approach in a consistent way, and only probability
    > >can result."
    >
    > >If you are asserting that fuzzy logic, if implemented in some
    > >appropriate manner must collapse to probability, then you may be right.
    > >I don't know. But I am not clear on why this would imply that actual
    > >fuzzy logic systems can't work.
    >
    > No, what I am saying is that "fuzziness" will be
    > incorporated into probability, or it cannot assist in
    > attaining a course of action. It is that the fuzzicists
    > collapse probability, not that fuzziness collapses into
    > probability.
    > --
    > This address is for information only. I do not claim that these views
    > are those of the Statistics Department or of Purdue University.
    > Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
    > hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558

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