Triangular MF

Triangular membership function

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Libraries:
Fuzzy Logic Toolbox / Membership Functions

Description

The Triangular MF block implements a triangle-shaped membership function.

$$f\left(x;a,b,c\right)=\left\{\begin{array}{ll}0,\hfill & x\le a\hfill \\ \frac{x-a}{b-a},\hfill & a\le x\le b\hfill \\ \frac{c-x}{c-b},\hfill & b\le x\le c\hfill \\ 0,\hfill & c\le x\hfill \end{array}\right\}$$

More compactly, the function is as follows.

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

The parameters a and c set the left and right feet or base points of the triangle. The parameter b sets the location of the triangle peak.

This block is related to the Trapezoidal MF, Linear S-shaped MF, and Linear Z-shaped MF blocks.

Ports

Input

x — Input value

scalar | vector

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

Output

MF — Membership value

scalar | vector

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

Parameters

Left base point a — Left foot of triangle

1 (default) | scalar

Left foot a of the triangle.

Programmatic Use

Block Parameter: a

Type: string, character vector

Default: "1"

Peak location b — Triangle peak

3 (default) | scalar

Triangle peak b.

Programmatic Use

Block Parameter: b

Type: string, character vector

Default: "3"

Right base point c — Right foot of triangle

6 (default) | scalar

Right foot c of the triangle.

Programmatic Use

Block Parameter: c

Type: string, character vector

Default: "6"

Extended Capabilities

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

PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.

Version History

Introduced before R2006a