## Nonlinear System VS Linear System

### Introduction

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.

### Matlab

In Matlab, this Bell-shaped function is defined as:

`y=dbellmf(x,params)`

Example:

`x=0:0.1:10;`

y=gbellmf(x,[2 4 6]);

plot(x,y)

xlabel('gbellmf, P=[2 4 6]')

### References & Resources

- Matlab - http://www.mathworks.co.uk/help/toolbox/fuzzy/gbellmf.html

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