evalmf

Evaluate fuzzy membership function

Syntax

y = evalmf(mfT1,x)

[yUpper,yLower] = evalmf(mfT2,x)

Description

This function evaluates type-1 and type-2 membership functions for specified input values and returns the corresponding membership values.

y = evalmf(mfT1,x) evaluates one or more type-1 membership functions based on the input values in x, returning the membership function values.

[yUpper,yLower] = evalmf(mfT2,x) evaluates one or more type-2 membership function based on the input values in x, returning both the upper and lower membership function values.

Examples

Evaluate Membership Function

Evaluate a generalized bell-shaped membership function across a range of input values from 0 through 10.

x = 0:0.1:10;
mf = fismf("gbellmf",[2 4 6]);
y = evalmf(mf,x);

Plot the evaluation.

plot(x,y)
xlabel("gbellmf, P = [2 4 6]")

Evaluate Multiple Membership Functions

Create a vector of three Gaussian membership functions.

mf = [fismf("gaussmf",[0.9 2.5],Name="low");
      fismf("gaussmf",[0.9 5],Name="medium");
      fismf("gaussmf",[0.9 7.55],Name="high")];

Specify the input range over which to evaluate the membership functions.

x = (-2:0.1:12)';

Evaluate the membership functions.

y = evalmf(mf,x);

Plot the evaluation results.

plot(x,y)
xlabel("Input (x)")
ylabel("Membership value (y)")
legend("low","medium","high")

Evaluate Type-2 Membership Function

Create a triangular type-2 membership function.

mf = fismftype2("trimf",[5 7 9],LowerLag=0.3,LowerScale=0.8);

Evaluate the membership function across a range of input values from 0 through 10.

x = 0:0.1:10;
[yUpper,yLower] = evalmf(mf,x);

Plot the evaluated upper and lower MFs.

plot(x,yUpper,x,yLower)
legend("Upper MF","Lower MF",Location="northwest")
xlabel("Input")
ylabel("Membership value")

Input Arguments

mfT1 — Type-1 membership function

fismf object | vector of fismf objects

Type-1 membership function, specified as a fismf object or a vector of such objects.

x — Input value

scalar | vector | 2-D matrix

Input value, specified as a scalar, vector, or 2-D matrix. If mf is a:

• Single fismf object, then you can specify x as a scalar, vector, or matrix

• Vector of fismf objects, then you can specify x as a scalar or vector

mfT2 — Type-2 membership function

fismftype2 object | array of fismftype2 objects

Type-2 membership function, specified as a fismftype2 object or a vector of such objects.

Output Arguments

y — Membership values for a type-1 membership function

scalar | vector | 2-D matrix

Membership value for a type-1 membership function, returned as a scalar, vector, or 2-D matrix. If mfT1 is a:

• Single fismf object, then y is a scalar, vector, or matrix with the same dimensions as x. Each element of y is the evaluated membership value for the corresponding element of x.

• Vector of fismf objects, then y is an M-by-N matrix, where M and N are the lengths of mfT1 and x, respectively. y(i,j) is the evaluated value of membership function mfT1(i) for input value x(j).

yUpper — Upper MF membership values for a type-2 membership function

scalar | vector | 2-D matrix

Upper MF membership value for a type-2 membership function, returned as a scalar, vector, or 2-D matrix. If mfT2 is a:

• Single fismftype2 object, then y is a scalar, vector, or matrix with the same dimensions as x. Each element of y is the evaluated membership value for the corresponding element of x.

• Vector of fismftype2 objects, then y is an M-by-N matrix, where M and N are the lengths of mfT2 and x, respectively. y(i,j) is the evaluated value of membership function mfT2(i) for input value x(j).

yLower — Lower MF membership values for a type-2 membership function

scalar | vector | 2-D matrix

Lower MF membership value for a type-2 membership function, returned as a scalar, vector, or 2-D matrix. If mfT2 is a:

• Single fismftype2 object, then y is a scalar, vector, or matrix with the same dimensions as x. Each element of y is the evaluated membership value for the corresponding element of x.

• Vector of fismftype2 objects, then y is an M-by-N matrix, where M and N are the lengths of mfT2 and x, respectively. y(i,j) is the evaluated value of membership function mfT2(i) for input value x(j).

Version History

Introduced before R2006a

R2018b: fismf object input argument

evalmf now takes a fismf object as an input argument rather than the type and parameters of the membership function. Also, you can now evaluate multiple membership functions by passing an array of fismf objects to evalmf. There are differences between these approaches that require updates to your code.

Update Code

Previously, you evaluated a membership function for given input values, x, by specifying the type of membership function, type, and the membership functions parameters, params.

y = evalmf(x,params,type);

Update your code to first create a fismf object, mf. Then, pass this object to evalmf.

mf = fismf(type,params);
y = evalmf(mf,x);

Also, previously, to evaluate multiple membership functions you called evalmf once for each membership function.

y1 = evalmf(x,params1,type1);
y2 = evalmf(x,params2,type2);
y3 = evalmf(x,params3,type3);

Now, you can evaluate multiple membership functions by passing an array of fismf objects to evalmf.

mf1 = fismf(type1,params1);
mf2 = fismf(type2,params2);
mf2 = fismf(type3,params3);
y = evalmf([mf1 mf2 mf3],x);

Here, y = [y1 y2 y3]';