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## Fuzzy Logic

#### Function

Modern electronically controlled automatic gearboxes no longer have a range selector for performance or economy mode. The control device determines, through the available sensors, whether the driver prefers to drive in the performance range or in the economic efficiency area. Now, how does the control device decide? A passenger would probably be more able to judge, after travelling a certain distance, whether the emphasis is placed on economy or on performance. To transfer the rules of human thinking to the computer, is the job of Fuzzy logic.

#### How it works

The word Fuzzy is spoken 'fasi' with a short 'a' and a soft 's' and means, more or less, 'blurred limit'. It was developed by Lofti A. Zadeh back in the 1980s at Berkley University. The above green diagram shows, as an example, how the temperature was until this point. All temperatures between 60°C and 80°C could only be designated to the categories 'cold' or 'hot'. However, that's exactly where the problem lies. Should not a temperature of 59.5°C also belong here? Leaps like this, probably grasp the reality only insufficiently. And how should one, using this method, judge an accelerator pedal position?

Therefore, the Fuzzy logic inserts, through an affiliation function, a variable (value between '0' and '1'). Then, using a certain affiliation function, the temperature 59.5°C, would be 'hot', using a different affiliation function, it could be categorised as 'warm'. The black diagram (above on the right) shows, in addition, various dependencies. The affiliation is shown mostly in the form of a triangle (blue), a trapezoid (red) or a normal distribution (brown). In between them, intersections occur where the values applied to the X-axis can be assigned to the one or the other area with different affiliation values. In this case, with the trapezoid, in the center of a certain X-area, the affiliation value 1, is reached.

In our example with the range selector, certain accelerator pedal positions with varying affiliation values, are assigned to certain areas (a small amount of gas, a little more gas etc.). In the same way other variables are included, e.g., the speed at which the accelerator pedal is operated. In the end, several variables with their affiliation values are calculated against each other, and the result is - although it concerns 'blurred' values, quite distinct, either performance or economy. 06/09

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