I have used fuzzy k-means. Aside from the ever present cluster validity problem it seems to seve the purpose. Among other things I used it for a pixel by pixle classification of multispectral images. The nice thing was that the memberships could be expressed a functions of the original image. john v verkuilen wrote:> 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