**7. Fuzzification, inference and defuzzification**

In order to complete the design of the controller, we need to define the fuzzification, inference and defuzzification procedures.

In most practical applications of fuzzy control, the fuzzification process used is the "singleton", where the membership function is characterized by having degree 1 for a single value of its universe (input value) and 0 for the rest. In other words, the impulse function could be used to represent a membership function of this type, Figure 9. It is especially used in implementations because in the absence of noise, the input variables are guaranteed to

Control Application Using Fuzzy Logic: Design of a Fuzzy Temperature Controller 391

Fig. 11. Fuzzy partition of the fuzzy controller inputs (error and error-variation) and output

Fig. 10. Fuzzy controller for the temperature system.

(increase command).

equal their measured value. We also avoid the calculations that would be required if another membership function were used, such as Gaussian fuzzification, which requires constructing a Gaussian-shaped membership function to represent the exact value being provided by the sensor.

Fig. 9. Fuzzification process for the controller's input variable.

In order to define the inference mechanism, we have to determine how to carry out the basic operations. Since we are using Mandani's model, we have decided to implement the T-norm as the minimum and the S-norm as the maximum.

The last step is to define the defuzzification process. For this temperature control case, we will use the center of gravity.
