[FOM] Fuzziness
Patrik Eklund
peklund at cs.umu.se
Thu Jul 21 04:22:03 EDT 2016
On 2016-07-21 00:08, Charlie wrote:
> Is there anything to the charge I’ve often heard that Fuzzy Logic is
> really probability theory requiring arbitrary assumptions?
This is a long-standing debate, that has so far never come to any sort
of conclusion.
In
http://www.glioc.com/files_glioc/FuzzySetsAndSignatures.pdf
you will find an (not necessarily 'the' but 'one') explanation of the
difference between probability, possibility and many-valued logic. This
note is a summary of postings I had provided within the BISC mailing
list over the last years before writing that note.
It has to be said that probability is not logical, and probability is
untyped. Probability may be seen closer to look like a propositional
logic, since probability leans on its "universe of samples", which is
just a set, or a set of names, and "events" which are just sets as
elements in a sigma-algebra. And so on. Probability then is capable of
responding to "how many?" on a population (again a set) basis, but not
capable of responding to "how?" which often is more like rule and
sequence.
This is the dilemma of evidence-based medicine (EBM) where clinical
trials are based on sampling and population, but "evidence" as to appear
in clinical guidelines need to be designed so that they target
individuals. Probability remains logically two-valued in the sense that
belonging or not to a sample set is indeed bivalent, but in reality (in
clinical trials) some samples are "better" than others. Exclusion
criteria in sampling are also bivalent. Health is in my view an
excellent playground for connecting theory and practice, even as related
to foundational questions.
Best,
Patrik
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