Re: Fuzzy Logic & the Human Sciences

"Lionel Cox" <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> 
> Well I appear not to be able to find people who have worked with fuzzy in
> the human science field. By this I mean sociology. Could anyone please give
> me leads as to journal articles, papers, books that may cover this topic.
> Even better would be to 'talk' to people who have worked or studied this
> field of fuzzy.
> Lionel Cox

Max A. Woodbury created the "GoM" system for categorical data analysis
about 30 years ago that has been heavily used by the National
Institute on Aging over the last 20 years for analysis of the National
Long Term Care Study questionnaires, among many other applications. A
reference is Manton, Woodbury and Tolley (1994), "Statistical Analysis
using Fuzzy Sets", Wiley Inter-Science, New York.

We have J variables, each of which has L(j) categories. For
questionnaires, there are J questions and L(j) possible responses. We
have I subjects who have answered the questionaire.

We hypothesize that the subjects are mixtures of K idealized types,
the "pure types". To illustrate pure types, George Gaylord Simpson
wrote many years ago that there are three types of scientists: the
dreamer, who sits bny the side of a stream, whittles and thinks about
things; the lab mn, who wears a white coat and tends softly purring
machines; and the business man, who sits at his desk, answers the
telephone, writes grants and draws up budgets. "In fact," Simpson
said, "Every scientis is a comples mixture of the three." We have a
fuzzy set for each subject, with K members (the pure types). The
extent to which individual i manifests the characteristics of pure
type k is his grade of membership g(i,k), with sum over k (g(i,k) = 1.
The estimated probability that an individual of pure type k will give
reply l to question j is pi(j,k,l), with sum over l(pi(j,k,l) = 1.
Then the predicted probability that individual i will give response l
to question j, p(i,j,l), is given by

p(i,j,l) = sum over k(g(i,k)pi(k,j,l)

The model parameters, the g(i,k) and pi(k,j,l) are evaluated by
maximum likelihood.

Although this model is brilliant in its simplicity and demonstrated
power, it has been ignored by both fuzzy people and probabilists for
the same reason: it mixes probability and fuzzy, and of course it is
dogma that never the twain shall meet.

Since I am intimately acquainted with this work I would be glad to
discuss it with you via EMail or telephone.

Sncerely, William Siler