Nonlinear System VS Linear System
The generalized bell function depends on three parameters a, b and c as given by:
Each of these parameters has a physical meaning: c determines the centre of the corresponding membership function; a is the half width; and b (together with a) controls the slopes at the crossover points. Figure below shows these concepts.
Figure 2: The effects of changing parameters in bell function: (a) changing 'a'; (b) changing 'b'; (c) changing 'c'; (d) changing 'a' and 'b' simultaneously but keeping their ratio constant.
In Matlab, this Bell-shaped function is defined as:
y=gbellmf(x,[2 4 6]);
xlabel('gbellmf, P=[2 4 6]')
References & Resources
- Matlab - http://www.mathworks.co.uk/help/toolbox/fuzzy/gbellmf.html
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