Obtaining fuzzy membership (was Re: Thomas' Fuzziness and Probability)

From: john v verkuilen (jayv@uiuc.edu)
Date: Mon Aug 13 2001 - 21:52:32 MET DST

  • Next message: Robert Ehrlich: "Re: Fuzziness as opposed to Probability"

    William Chesters <williamc@paneris.org> writes:

    >Robert Ehrlich <bobehrlich@home.com> writes:
    >> IMHO fuzzy memberships reflect the degree of hybridness of samples and
    >> have nothing especially to do with prob.

    > But the only concrete suggestion you see in fuzzy logic books for how
    >to obtain fuzzy memberships numbers is to use the proportion of domain
    >experts who say the man is tall, or whatever.

    Indeed, which is something that many have justly criticized. There is a
    useful review in Michael Smithson's sadly overlooked gem of a book Fuzzy
    Set Analysis in Behavioral and Social Sciences. Klir and Yuan's textbook
    has some information on what they call "direct" and "indirect" methods. You
    are right to note that nearly all methods used are direct methods, which are
    basically just expert ratings (with many or only one expert). They note a few
    possible indirect methods, including one based on eigenvalue decompositions
    of paired comparison matrices due to Saaty and a suggestion on using neural
    nets, though I don't remember any details.

    In some recent correspondence, Smithson and I discussed this issue. (My
    dissertation is on use of fuzzy set theory in social sciences and Smithson
    is the expert in the field.) I proposed using dual scaling for assigning
    membership from multiple categorical indicators. Actually an old Biometrika
    article by Harvey Goldstein solved much of the problem, though there was no
    connection with fuzzy sets. We discussed the possibility of using IRT models
    as well.

    I hope my own research on this topic will see publication (finishing the
    dissertation comes first, though, so there are other parts to write :) but
    if you're interested, please see:
    http://ux6.cso.uiuc.edu/~jayv/verkuilenAPSA2001.pdf.

    Jay

    --
    J. Verkuilen						jayv@uiuc.edu
    "Depend upon it, sir, when a man knows he is to be hanged in a fortnight, it
    concentrates his mind wonderfully."  --Dr. Samuel Johnson
    Dissertation pages written: 58
    

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