Fuzzy rule evaluation

As a result of fuzzy rule evaluation, each analog output variable is represented by several fuzzy variables. The purpose of defuzzification is to obtain analog outputs. This can be done by using a membership function similar to that shown in Fig. 19.32. In the first step, fuzzy variables obtained from rule evaluations are used to modify the membership function employing the formula... 

Fuzzy reasoning involves two parts evaluating the rule antecedent (the IF part of the rule) and applying the result to the consequent (the THEN part of the rule). Like the rules in expert systems, a fuzzy rule can have multiple antecedents joined by fuzzy operators AND or OR, or multiple consequents joined by fuzzy operator AND. For example ... 

After input data are fuzzified and their membership values obtained, the next step involves application of them to the antecedents of fuzzy rules. If a given fuzzy rule has multiple antecedents, a fuzzy operator (AND or OR) is used to obtain a single number that represents the result of antecedent evaluation. This number is then applied to a consequent membership function. 

AND is used to evaluate the conjunction of rule antecedents. Typically, fuzzy logic systems utilize the classical fuzzy operation intersection to implement this operation. Consider fuzzy rule 1 ... 

Similarly, OR is used to evaluate the disjunction of rule antecedents, which is implemented by the classical fuzzy operation union in fuzzy logic systems. Consider fuzzy rule 2 ... 

To get a feel of the fuzzy definition set, detection likelihood, as shown in Fig. lV/2.2.3-1, has been transformed into a fuzzy definition. A typical fuzzy membership is shown in Fig. lV/2.6.4-2. Actual fuzzy values are derived based on the fuzzy rule set. Fuzzy inputs are evaluated using a rule-based set, so that criticality and RPN calculations can be made. In the fuzzification process, with help of crisp ranking, set S O D is converted into fuzzy representation so that these can be matched with the rule base. Here, the if then rule has two parts an antecedent (which is compared to input) and consequence (which is the result). On the other hand, in the defuzzification process, the reverse takes place. It is possible to automate FMEA using fuzzy logic and rule-based systems. The rule allows quantitative data such as occurrence to be easily combined with judgmental and quantitative data (such as severity and detectability) very easily and uniformly. The rule based on the linguistic variables is more expressive and useful (for further reading see Ref. [11]). 

By making fuzzy evaluations, with zero at the bottom of the scale and 1.0 at the top, one can have an analysis rule basis for the fuzzy logic method, and s/he can accomplish analysis or control project. The results seem to turn out well for complex systems or systems where human experience is the only base from which to proceed, certainly better than doing nothing at all, which is where one would be if unwilling to proceed with fuzzy rules. 

Rule evaluation (Application of fuzzy mles, also known as inference) ... 

The marine industry is recognising the need for powerful techniques that can be used to perform risk analysis of marine systems. One technique that has been applied in both national and international marine regulations and operations is Failure Mode and Effects Analysis (FMEA). This risk analysis tool assumes that a failure mode occurs in a system/component through some failure mechanism. The effect of this failure is then evaluated. A risk ranking is produced in order to prioritise the attention for each of the failure modes identified. The traditional method utilises the Risk Priority Number (RPN) ranking system. This method determines the RPN by finding the multiplication of factor scores. The three factors considered are probability of failure, severity and detectability. Traditional FMEA has been criticised to have several weaknesses. These weaknesses are addressed in this Chapter. A new approach, which utilises the fuzzy rules base and grey relation theory, is presented. 

When we have evaluated all the rules, an output variable might belong to two or more fuzzy subsets to different degrees. For example, in the enzyme problem one rule might conclude that the rate is low to a degree of 0.2 and another that the rate is low to a degree of 0.8. In aggregation, all the fuzzy values that have been calculated for each output variable are combined to provide a consensus value for the membership of the output variable in each... 

In order to combine the conclusions of several such Fuzzy Inference Systems, they will be translated into belief structures, according to the method proposed in [22]. Each Fuzzy Inference System presented Figure 12 is the association of fuzzification functions (providing a numerical evaluation of the membership of a variable to fuzzy sets) and of rules linking these observations to different classes which can be states or disjunctions of states of the process. 

Now to determine the output weight Wo for a specific input Vo, AND operation is performed between hal Vo) and the general result HALnBniv, w) evaluated at Vq according to fuzzy if-then rule-1. Let it be Qi(w). Similarly Qxiw) an Qsiw) are calculated for rule-2 and rule-3 respectively. 

The meaning of the application of fuzzy models in risk analysis is to provide mathematical formulations that could characterize the uncertain parameters involved in complex safety evaluation me ods. Fuzzy logic is a decisional system based on linguistic rules once the membership functions have been defined for all the fuzzy variable sets, each set has to be connect by... 

Fuzzifier. Fuzzifier maps crisp inputs into type-2 fuzzy sets by evaluating the crisp inputs x= xi,X2,..., x ) based on the antecedent part of the rules and assigns each crisp input to its type-2 fuzzy set A(x) with its membership grade in each type-2 fuzzy set. 

Table 1. Fuzzy reasoning rules for the TIP Evaluation local model. 

The output variable of the local fuzzy reasoning model for TIP evaluation is presented in Figure 6. This variable is at the same time the input variable for the device evaluation model. The example assumed fuzzy reasoning rules are shown in Table 1. 

A more complex fuzzy relationship can provide a better description. However, the observed behavior of the net growth rate is not so complex that a more complex fuzzy relationship is justified from a transparency point of view. A final evaluation of the fuzzy model should be done after integration in the hybrid model structure. Although fuzzy logic is a black box technique, a posteriori analysis of the model shows that the three rules represent three phases during a batch. 

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