Fuzzy Expert System Model

A fuzzy expert system  consists of four components namely, the fuzzifier, the inference engine, and the defuzzifier, and a fuzzy rule base.


Fuzzy Expert System Model

In the fuzzifier, crisp inputs are fuzzified into linguistic values to be associated to the input linguistic variables. After fuzzification, the inference engine refers to the fuzzy rule base containing fuzzy IF-THEN rules to derive the linguistic values for the intermediate and output linguistic variables. Once the output linguistic values are available, the defuzzifier produces the final crisp values from the output linguistic values.

Fuzzification

Through the use of membership functions defined for each fuzzy set for each linguistic variable, the degree of membership of a crisp value in each fuzzy set is determined. As an example below, the numerical variable age which has a given value of 25.0 was fuzzified using the triangular membership functions defined for each fuzzy set for linguistic variable age. As a result of fuzzification, linguistic variable age has linguistic values of "young" with a degree of membership of 0.666, "quite old" with a degree of 0.333, and for the remaining linguistic values with a degree of 0.0.


Sample fuzzification of crisp inputs

In a fuzzy expert system application, each input variable's crisp value is first fuzzified into linguistic values before the inference engine proceeds in processing with the rulebase.

Fuzzy Rule Base and Fuzzy IF-THEN Rules

Fuzzy expert systems use fuzzy IF-THEN rules. A fuzzy IF-THEN rule is of the form

IF X1 = A1 and X2 = A2 ... and Xn = An THEN Y = B
where Xi amd Y are linguistic variables and Ai and B are linguistic terms. The IF part is the antecedent or premise, while the THEN part is the consequence or conclusion. An example of a fuzzy IF-THEN rule is
IF pressure = "low" THEN volume = "big"
The following are some examples of rules used in the Investor Profile application available in this site:
IF (age = "young") and (fund = "small") THEN (tolerance = "risk neutral")
IF (age = "quite old") and (fund = "large") THEN (tolerance = "venturesome")
IF (fund = "very large") THEN (tolerance = "venturesome")
In a fuzzy expert system, the collection of fuzzy IF-THEN rules is stored in the fuzzy rule base which is referred to by the inference engine when processing inputs.