In article <3B69AD4E.815FAA76@gao.gov>, Art Kendall <kendalla@gao.gov> wrote:> Fuzzy logic has many different meaning, but I think of a couple of areas > where membership in a group is better represented by a number between zero > and one than by just zero or one.
> In cluster analyses of profiles of patients Lorr found that some were close > to the centroid of schizophrenics, some close to the centroid of paranoids > and some "sort of like both".
> In the classification phase of a discriminant function analyis the casewise > listings have a set of columns that show the probability that each case is a > member of each of the groups.
> In an R factor analysis, when items are put on scales, unit weights are > customarily used. But the weights are not just zeros and ones.
> In a Q factor analysis, a case is classified into a group based on its > highest loading, but the loadings on each factor are continuous.
> In a way, many pattern detection or pattern recognition approaches have some > "fuzzy logic" as opposed to integer valued logic.
So how do you use this to DECIDE what to do? You do not just use 0-1 logic; integer valued logic is no different from rational with an appropriate scale. As a truth-value system, it just does not work. Probability is not a truth-value system, either, but a scale imposed on a Boolean system. Complete a "fuzzy" approach in a consistent way, and only probability can result. -- 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