[FOM] Fuzziness

Daniel Schwartz schwartz at cs.fsu.edu
Thu Jul 21 13:11:54 EDT 2016

Fuzzy sets theory is sometimes characterized as being more general than
probability theory because it does not require that the fuzzy values
associated with the events in an event space add up to 1; the sum can be
greater than 1.

A nice analysis of the similarites and differences is:

D. Dubois and H. Prade, Fuzzy sets and probability: Misunderstandings,
bridges and gaps, in Proceedings of the Second IEEE Conference on Fuzzy
Systems, 1993.

Fuzzy logic is actually more akin to Lukasiewicz infinitary logic than to
probability theory.  My doctoral dissertation produced axioms for a core
fragment of this logic.  This was later published as:

D.G. Schwartz, Axioms for a theory of semantic equivalence.  {\it Fuzzy Sets
and Systems}, 21 (1987) 319--349.

--Dan Schwartz

Dr. Daniel G. Schwartz                            Office    850-644-5875
Dept. of Computer Science, MC 4530                CS Dept   850-644-4029
Florida State University                          Fax       850-644-0058
Tallahassee, FL 32306-4530                        schwartz at cs.fsu.edu
U.S.A.                                   http://www.cs.fsu.edu/~schwartz

Charlie <silver_1 at mindspring.com> wrote:

> 	  Is there anything to the charge I???ve often heard that Fuzzy Logic is really probability theory requiring arbitrary assumptions?

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