Subject: [11] Are there fuzzy state machines?

Date: 15-APR-93


Yes. FSMs are obtained by assigning membership grades as weights to the states of a machine, weights on transitions between states, and then a composition rule such as MAX/MIN or PLUS/TIMES (see [4]) to calculate new grades of future states. Refer to the following article, or to Section III of the Dubois and Prade's 1980 textbook (see [16]).


Gaines, Brian R., and Kohout, Ladislav J., "Logic of Automata", Int. J. Gen. Sys. 2(4):191-208, 1976.



Subject: [12] What is possibility theory?

Date: 15-APR-93


Possibility theory is a new form of information theory which is related to but independent of both fuzzy sets and probability theory. Technically, a possibility distribution is a normal fuzzy set (at least one membership grade equals 1). For example, all fuzzy numbers arepossibility distributions. However, possibility theory can also be derived without reference to fuzzy sets.


The rules of possibility theory are similar to probability theory, but use either MAX/MIN or MAX/TIMES calculus, rather than the PLUS/TIMES calculus of probability theory. Also, possibilistic NONSPECIFICITY is available as a measure of information similar to the stochastic




Possibility theory has a methodological advantage over probability theory as a representation of nondeterminism in systems, because the PLUS/TIMES calculus does not validly generalize nondeterministic processes, while MAX/MIN and MAX/TIMES do.


For further information, see:


Dubois, Didier, and Prade, Henri, "Possibility Theory", Plenum Press, New York, 1988.


Joslyn, Cliff, "Possibilistic Measurement and Set Statistics", in Proceedings of the 1992 NAFIPS Conference 2:458-467, NASA, 1992.


Joslyn, Cliff, "Possibilistic Semantics and Measurement Methods in Complex Systems", in Proceedings of the 2nd International Symposium on Uncertainty Modeling and Analysis, Bilal Ayyub (editor), IEEE Computer Society 1993.


Wang, Zhenyuan, and Klir, George J., "Fuzzy Measure Theory", Plenum Press, New York, 1991.


Zadeh, Lotfi, "Fuzzy Sets as the Basis for a Theory of Possibility", Fuzzy Sets and Systems 1:3-28, 1978.



Subject: [13] How can I get a copy of the proceedings for <x>?

Date: 15-APR-93


This is rough sometimes. The first thing to do, of course, is to contact the organization that ran the conference or workshop you are interested in. If they can't help you, the best idea mentioned so far is to contact the Institute for Scientific Information, Inc. (ISI), and check with their Index to Scientific and Technical Proceedings (ISTP volumes).


Institute for Scientific Information, Inc.

3501 Market Street

Philadelphia, PA 19104, USA

Phone: +1.215.386.0100

Fax: +1.215.386.6362


Telex: 84-5305