Fuzzification process

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. 

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]). 

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. 

Fuzzification is the process of mapping crisp input xElU into fuzzy set f G U. This is achieved with three different types of fuzzifier, including singleton fuzzifiers, Gaussian fuzzifiers, and trapezoidal or triangular fuzzifiers. These fuzzifiers map crisp input x into fuzzy set with different membership functions pfix) listed below. 

Within the scope of the reasoning process we will use the input value fuzzification block, reasoning block using a number of rules and the defuzzi-... 

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) ... 

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. 

Fuzzy control uses experience instead of differential equations to determine desirable control actions. Fuzzy control consists of implementation of rules, in the format of IF... THEN statements, which relate the input variables to the control action. The process begins by first defining membership functions to classify the inputs and outputs using linguistic terms. In structural control applications, the inputs are usually a combination of structural responses displacement, velocity, and acceleration. The input values are then converted to fuzzy values, using the membership functions. This step is referred to as fuzzification. The next step is... 

In contrast, a fuzzy set of HOT temperatures can be defined. This fuzzy subset can cover a range of temperatures as did the bivalent set, but now the degree to which a measured data point falls into the fuzzy set of HOT is indicated by a "fit" value (/uzzy unit) between zero and one. The fit value is sometimes called the "degree of membership." Figure 5 shows examples of various fuzzy subsets or "membership functions" of the temperature. Depicted is the degree of membership of various temperatures to the fuzzy subsets COLD, WARM, and HOT. The process of assigning membership functions to sets of data is referred to as "fuzzification" of the data. 

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