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