Application of Fuzzy Rules

In a conventional expert system, the only rules to fire are those for which the condition is met. In a fuzzy system, all of the rules fire because all are expressed in terms of membership, not the Boolean values of true and false. Some rules may involve membership values only of zero, so have no effect, but they must still be inspected. Implicitly, we assume an or between every pair of rules, so the whole rule base is 

In order to reason using fuzzy data, a way must be found to express rules so that the degree of certainty in knowledge can be taken into account and a level of certainty can be ascribed to conclusions. This is done through fuzzy rules. A fuzzy rule has the form  

Once the input data have been used to find fuzzy memberships, in the second step we compute the membership value for each part in the condition or antecedent of a rule. These are then combined to determine a value for the conclusion or consequent of that rule. If the antecedent is true to some degree, the consequent will be true to the same degree. 

We have seen above that the fuzzified inputs are 

With these values, we can immediately evaluate rule R3. 

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Pongracz R, Bogardi I, Duckstein L (1999) Application of fuzzy rule-based modelling technique to regional drought. J Hydrol 224 100-114... 

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