Fuzzification. To determine the location of the transition from blood to myocardium or from myocardium to air, gray values are first classified. To ensure modality indepen- dence, only relative gray value differences between blood, myocardium and air are used. This makes Fuzzy C-Means (FCM) clustering a suitable algorithm to distinguish between three classes, and use the class transitions as borders. The classes used are bright, dark, and medium bright, which represent blood pool, air and myocardium respectively. To obtain a balanced class distribution, FCM was applied to the intersection rings from all the images simultaneously.
Fuzzification. In our fuzzy representations the partitions and clusters of the partitioning and clustering gp algorithms are converted into fuzzy sets by a process called fuzzification. The fuzzification process (see Figure 4.3) used here is based on the method that was used for fuzzy association rule mining in [48, 80]. We first select all the numerical attributes and cluster or partition each attribute’s possible values into a finite and fixed maximum number of partitions or clusters as described in Sections 3.3 and 3.4. Once we have determined the “Boolean” clusters and partitions we can convert them into fuzzy sets using fuzzy membership functions. Fuzzification
Fuzzification. Consider a fuzzy temperature controller with two inputs. The two inputs are the temperature T and the change i n temperature T. The actual measured temperature T and the calculated change in temperature T = Told - T are crisp values. For a classical temperature controller (e.g. PID) only the error in temperature is used as an input. The output o f this PID-controller is the actual control action for a control unit (e.g. heating system). If a fuzzy temperature controller, represented by fuzz y terms, is used, then it is necessary to convert (o r transform) the current i nputs into fuzzy inputs by finding the degrees of membership (fuzzy truth values) for al l input membership functions. This conversion from th e crisp inpu t space into the fuzzy input space is called fuzzification. The two inpu t variables T and T are cal led linguistic variables, an d each of these variabl es consist of a few membershi p functions (fuzzy terms). The membership function s (MFs) are assig xxx by the system designer (figure 48) , and are given la bels such as cold, warm for T and negative, zero, positive for T. Each of these label s represent a fuzzy set positioned in the operationa l domain (universe of discourse) of possible crisp values. In figure 48 the fuzzification process for input values of T = 10°C and T = -2°C/time unit (shown on the x - axis). The degree of membersh ip is the grade value at the intersection the system input value makes with a membership function. cold warm µ 0.75 µ 0.8 negative zero positive 0.25 0 T=10 40 -10 ) T= -2 0 10 T / [°C] ) T / [°C/time] Fig. 48: Fuzzification for two input variables. In figure 48 this yields a fuzzy input value for T of 0.75 for MF 'cold', and of 0.25 for M F 'w arm'. This process is repeated for the change of temperature input yielding 0.2 for MF 'negative', 0.8 for 'zero', and zero for M F 'positive'.
