Fuzzy Expert System
MEDEX makes use of expert system and fuzzy set
What is an expert system?
Human knowledge about prediction and
classification can often be expressed as a set of
heuristics or "rules-of-thumb." An expert
system involves the collection and encoding of these
rules, together with an inference engine for
evaluating the rule base for a given set of inputs.
In the case of MEDEX, a panel of experts in
Mediterranean weather forecasting assembled synoptic
rules-of-thumb predicting gale-force wind events for
the MEDEX wind types.
The rules were derived primarily from Brody and
Nestor (1980). One sample rule for the onset of a
gale-force mistral is as follows:
surface pressure difference between Location 1 (40N,
24E) and Location 2 (37N, 27E) is LARGE
AND: a surface low
pressure center or trough exists in the Gulf of Genoa
off the southern France coast
THEN: a gale-force Mistral
event is LIKELY
What is a fuzzy set?
A fuzzy set is a set whose elements might only
partially belong to that set, as opposed to the more
traditional nonfuzzy set, where the elements are
either completely inside or completely outside of the
set. The diagrams below illustrate the differences.
In the nonfuzzy definition diagram below, for a set
of small (weak) pressure gradients, all values less
than or equal to 5 mb belong to a designated set
completely, and all values greater than 5 mb do not
belong to that set at all. For the fuzzy definition
diagram below, for a set characterized as SMALL
pressure gradients, while 2 mb and 3 mb may belong
completely (100%) to SMALL, 4 mb may only belong to
SMALL to degree of 75%, and 5 mb to degree of 50%. As
a result, the fuzzy set allows for a smoother
transition out of SMALL for pressure gradient ranging
between 3 mb and 7 mb, as shown in the right portion
of the graph.
For more detailed information on fuzzy set theory,
refer to Zadeh (1983) and Kandel (1992).
How do fuzzy sets help MEDEX?
Fuzzy set methodology allows imprecision in user
input as well as imprecision in the expert system
rule base specification. In MEDEX, fuzzy sets allow
the user to indicate uncertainty or imprecision in
the degree of presence of particular synoptic
features specify range. While a non-fuzzy user input
may only be "yes" or "no", a
fuzzy input allows a range of input, from 0
("absolutely not") to 4 ("definitely
yes"). Furthermore, the rules-of-thumb are
expressed in terms of fuzzy sets, so that thresholds
("Is pressure gradient less than 5mb?") are
replaced by fuzzy sets ("Is pressure gradient
SMALL?"). Finally, non-fuzzy output allows only
"will occur" and "will not occur"
results, while fuzzy output will be a number between
0% and 100% indicating an estimated probability of
Brody, L. R. & Nestor, M.J.R. (1980). Regional
Forecasting Aids for the Mediterranean Basin
(Handbook for Forecasters in the Mediterranean, Part
2). Naval Research Laboratory, 7 Grace Hopper Avenue,
Monterey, California, 93943-5502, 178 pp.
Kandel, A. (1992). Fuzzy Expert Systems, CRC
Press, Boca Raton, FL, 314 pp.
Zadeh, L.A. (1983). The role of fuzzy logic in the
management of uncertainty in expert systems. Fuzzy
Sets Syst., 11: 199.