Linear Z-shaped MF

Linear z-shaped saturation membership function

Since R2022a

• 

Libraries:
Fuzzy Logic Toolbox / Membership Functions

Description

The Linear Z-Shaped MF block implements a linear z-shaped saturation membership function.

• When a < b:

  $$f\left(x;a,b\right)=\left\{\begin{array}{ll}1,\hfill & x<a\hfill \\ \frac{a-x}{a-b},\hfill & a\le x\le b\hfill \\ 0,\hfill & x>b\hfill \end{array}\right\}$$

• When a = b:

  $$f\left(x;a,b\right)=\left\{\begin{array}{cc}1,& x<a\\ 0,& x\ge a\end{array}\right\}$$

The parameters a and b control the shoulder and foot of the membership function, respectively. Setting a equal to b produces a crisp membership function.

This block is related to the Triangular MF, Trapezoidal MF, and Linear S-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 point a — Leftmost point of transition area

4 (default) | scalar

Leftmost point a of the transition area.

Programmatic Use

Block Parameter: a

Type: string, character vector

Default: "4"

Right point b — Rightmost point of transition area

6 (default) | scalar

Rightmost point b of the transition area.

Programmatic Use

Block Parameter: b

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 in R2022a