Rule Evaluation and Defuzzification

Rules are evaluated using min-max inferencing to calculate a numerical conclusion to the linguistic rule based on their input value (Zadeh (1992)). The result of this process is called the fuzzy risk conclusion. 

The truth value of a rule is determined from the conjunction (i.e. minimum degree of membership of the rule antecedents) (Zadeh (1973)). Thus the trath-value of the rule is taken to be the smallest degree of tmth of the rule antecedents. This tmth-value is then applied to all consequences of the rule. If any fuzzy output is a consequent of more than one rule, that output is set to the highest (maximum) tmth-value of all the mles that include it as a consequent. The result of the mle evaluation is a set of fiizzy conclusions that reflect the effects of all the mles whose tmth-values are greater than zero. 

Consider the risk priority table (Table 6.2) where the probability of occurrence is High , the severity is Marginal and their associated degrees of belief are 0.6 and 1.0, respectively. Thus the conclusion Riskiness = Important has a membership value of min (0.6.1.0) = 0.6. To establish how risky the hazard is, this fuzzy conclusion has to be defiizzified to obtain a single crisp result. 

The defuzzification process creates a single assessment from the fiizzy cmiclusion set expressing the risk associated with the event, so that corrective actions can be prioritised. Several defuzzification techniques have been developed (Runkler and Glesner (1993)). One conunon technique is the weighted mean of maximum method, which is illustrated here. This technique averages the points of maximum possibility of each fuzzy conclusion, wei ted by their degrees of truth. Hence, if the conclusion fixrm the risk evaluation phase is, for example, 0.5 Low, 0.1 Low and 0.5 Mod, the maximum value for each linguistic term is taken. This reduces the conclusion to 0.5 Low and 0.5 Mod to be defuzzified. 

The following is given to demonstrate how riskiness is obtained. Suppose event A has the following probability of occurrence and severity of consequences  

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