gbellmf

Generalized bell-shaped membership function

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Syntax

y = gbellmf(x,params)

Description

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

y = gbellmf(x,params) returns fuzzy membership values computed using the following generalized bell-shaped membership function:

f(x;a,b,c)=11+|x−ca|2b

To configure the membership function, specify parameters, a, b, and c using params.

Membership values are computed for each input value in x.

example

Examples

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Open Live Script

Specify input values across the universe of discourse.

x = 0:0.1:10;

Evaluate membership function for the input values.

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

Plot the membership function.

plot(x,y)
title("gbellmf, P=[2 4 6]")
xlabel("x")
ylabel("Degree of Membership")
ylim([-0.05 1.05])

Figure contains an axes object. The axes object with title gbellmf, P=[2 4 6], xlabel x, ylabel Degree of Membership contains an object of type line.

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].

Here:

  • a defines the width of the membership function, where a larger value creates a wider membership function.

  • b defines the shape of the curve on either side of the central plateau, where a larger value creates a more steep transition.

  • c defines the center of the membership function.

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 gbellmf membership function.

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

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

Extended Capabilities

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C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced before R2006a

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See Also

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