Defuzzification process

Notice that the fuzzy probability distribution function presented in Fig. 4 represents the possibility function related to the probabilities of operator success and failure. Nevertheless, these possibilities functions are in the linguistic domain and must be translated to the real domain. To achieve this, the defuzzification process presented by Chen and KJien (1997) has to be used. 

FIGURE 19.32 Fuzzification process (a) typical membership functions for the fuzzification and the defuzzification processes, (b) example of converting a temperature into fuzzy variables. 

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]). 

Center of gravity method ( Centroid name is used in Matlab software) was used in output variables defuzzification process (because all active rules are used in defuzzification process). It improved model sensitivity on input parameters change. Disadvantage of center of gravity method is large amount of calculation (because irregular shaped... 

The defuzzification process relies on the approach to calculating the union of the fuzzy terms of all the consequents. Further, the center of gravity of the union is calculated to be the final output correction. 

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. 

An inference system commonly used to develop fuzzy models is the Mamdani fuzzy inference system. The Mamdani approach was developed in the 1970s and was the first inference method applied to control systems [15]. The Mamdani inference procedure describes the output variables as fuzzy sets. The approach uses max-min composition in which the minimum of the two antecedents is taken for a particular rule and the maximum combination of the rules is determined for aggregating the effects of aU the rules. The effect of the max combiner on the output membership functions is to generate an "envelope" of the fired output membership functions. In order to defuzzify this output set, the centroid (weighted average) of the envelope is found by integrating over the 2-dimensional shape. The defuzzification process of the Mamdani approach is computationally intensive. 

Fuzzy control is reahzed within 3 processes fuzzification, inference and defuzzification. The fuzzification process describes variables by means of input values. Thus a fuzzy set is represented by a membership function. The membership function is constructed based on the variable s input values (laanineh Maijohann 1996). Accordingly every input value obtains a membership degree between one and zero. If the input value is clearly assigned to the description of the variable, it receives a membership degree one. It is a fiiU membership to a related fuzzy set. The membership degree zero means that an input value does not belong to the fuzzy set. Membership values between zero and one indicate a partial membership of an input value to the certain fuzzy set. 

Type-2 fuzzy logic systems are rule-based systems that are similar to type-1 fuzzy logic systems in terms of the structure and components but a type-2 fuzzy logic system has an extra output process component which is called the type-reducer before defuzzification as shown in Fig. 5.3. The type-reducer reduces outputs type-2 fuzzy sets to type-1 fuzzy sets and then the defuzzifier reduces them to crisp outputs. The components of a type-2 Mamdani fuzzy logic system are [26] ... 

In the reasoning process we use the input values fuzzification block, then inference block that uses a set of fuzzy rules, and finally defuzzification block of output values. The set of rules is being created with experts opinions, in this case aircraft pilots and people responsible for Safety Management System (SMS) organization. As a inference rule for local models we will use the fuzzy rule modus ponens, as below (Kacprzyk 1986) ... 

By weighting, fine-tuning of the consequents of the mles is possible, without changing the reference fuzzy sets. This process is called defuzzification. 

Defuzzification - Matching data from the pre-processing stage with the data from the training set. 

Figure 16.21 shows the main blocks of the fuzzy system which is the main part of the fuzzy logic controller (Lee, 1990 Passino and Yurkovich, 1998). The fuzzification block converts the inputs or physical variables, for instance the error signal, e(t), into suitable fuzzy sets, as was shown in the example of Figure 16.20. fuzzy inference process combines membership functions with the control rules to derive the fuzzy output, for example, the fuzzy controller output, u(t). This process is also often called fuzzy reasoning. Finally, these outputs of the fuzzy computations are translated into terms of real values using the defuzzification block. 

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