# Objective Meaning of Fuzzy sets

Hans Wehn (hwehn@Direct.CA)
Tue, 5 Mar 1996 19:21:10 +0100

I am relatively new to Fuzzy Logic. One thing that always puzzled
me is the apparent absense of an objective experimental meaning of fuzzy sets.
For example, can I perform an objective experiment that lets me conclude that the
membership degree of a 1.80m tall man in the set of "tall" men is, say, 0.8 rather
than 0.001 ? In other words, when all I tell you is that I know a man has a
membership of 0.8 in the set of tall men, then do I actually convey to you
any information at all ?

One idea I had is to conduct a poll and ask people what membership degree
they would give a 1.80m tall man in the set of "tall" men. Then take the average
value as the true objective membership degree. Does this makes any sense ?
Even if it does, what about repeating this poll among a pygmy tribe. Their idea
of "tall" may be quite different from the North American value. Thus, does a 0.8
membership degree in the set of tall men have any objective meaning ?

It appears to me that if I use probability methods I can always force an objective
meaning by taking refuge in relative frequencies: In other words, I can at least
in principle perform experiments that would objectively validate an assumed
probability distribution. How do I do this when I subsribe to a Fuzzy method.

Similarly, if I use a Fuzzy system that in the end calculates that a variable has
the fuzzy value 0.8 then what exactly does this result tell me ? How can I
validate its meaning and correctness experimentally ?

Hans