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What Is Fuzzy Logic?

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2 Tutorial<br />

the Sugeno-type representation of the now-familiar tipping model. If you load<br />

thesystemandplotitsoutputsurface,youwillseethatitisalmostthesame<br />

as the Mamdani system you have previously seen.<br />

a = readfis('tippersg');<br />

gensurf(a)<br />

20<br />

tip<br />

15<br />

10<br />

10<br />

8<br />

6<br />

food<br />

4<br />

2<br />

0<br />

0<br />

2<br />

4<br />

service<br />

6<br />

8<br />

10<br />

The easiest way to visualize first-order Sugeno systems is to think of each rule<br />

as defining the location of a moving singleton. That is, the singleton output<br />

spikes can move around in a linear fashion in the output space, depending<br />

on what the input is. This also tends to make the system notation very<br />

compact and efficient. Higher-order Sugeno fuzzy models are possible, but<br />

they introduce significant complexity with little obvious merit. Sugeno fuzzy<br />

models whose output membership functions are greater than first order are<br />

not supported by <strong>Fuzzy</strong> <strong>Logic</strong> Toolbox software.<br />

Because of the linear dependence of each rule on the input variables, the<br />

Sugeno method is ideal for acting as an interpolating supervisor of multiple<br />

linear controllers that are to be applied, respectively, to different operating<br />

conditions of a dynamic nonlinear system. For example, the performance<br />

2-102

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