MEDEX: A Fuzzy Expert System

MEDEX makes use of expert system and fuzzy set technology.

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:

IF:         the 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 onset.

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.