# trapmf

Trapezoidal membership function

## Description

This function computes fuzzy membership values using a trapezoidal membership function. You can also compute this membership function using a fismf object. For more information, see fismf Object.

This membership function is related to the trimf, linsmf, and linzmf membership functions.

example

y = trapmf(x,params) returns fuzzy membership values computed using the following trapezoidal membership function:

$f\left(x;a,b,c,d\right)=\mathrm{max}\left(\mathrm{min}\left(\frac{x-a}{b-a},1,\frac{d-x}{d-c}\right),0\right)$

To define the membership function parameters, specify params as the vector [a b c d].

Membership values are computed for each input value in x.

## Examples

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Specify input values across the universe of discourse.

x = 0:0.1:10;

Evaluate membership function for the input values.

y = trapmf(x,[1 5 7 8]);

Plot the membership function.

plot(x,y)
title('trapmf, P = [1 5 7 8]')
xlabel('x')
ylabel('Degree of Membership')
ylim([-0.05 1.05])

## Input Arguments

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Input values for which to compute membership values, specified as a scalar or vector.

Membership function parameters, specified as the vector [a b c d]. Parameters b and c define the shoulders of the membership function, and a and d define its feet.

The shape of the membership function depends on the relative values of b and c.

• When c is greater than b, the resulting membership function is trapezoidal.

• When b is equal to c, the resulting membership function is equivalent to a triangular membership function with parameters [a b d].

• When c is less than b, the resulting membership function is triangular with a maximum value less than 1.

## Output Arguments

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Membership value returned as a scalar or a vector. The dimensions of y match the dimensions of x. Each element of y is the membership value computed for the corresponding element of x.

## Alternative Functionality

### fismf Object

You can create and evaluate a fismf object that implements the trapmf membership function.

mf = fismf("trapmf",P);
Y = evalmf(mf,X);

Here, X, P, and Y correspond to the x, params, and y arguments of trapmf, respectively.

## Version History

Introduced before R2006a

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