S-shaped MF

S-shaped membership function

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Libraries:
Fuzzy Logic Toolbox / Membership Functions

Description

The S-shaped MF block implements an s-shaped membership function.

$$f(x;a,b)=\left\{\begin{array}{ll}0,\hfill & x\le a\hfill \\ 2{\left(\frac{x-a}{b-a}\right)}^2,\hfill & a\le x\le \frac{a+b}{2}\hfill \\ \text{1}-\text{2}{\left(\frac{x-b}{b-a}\right)}^{\text{2}},\hfill & \frac{a+b}{2}\le x\le b\hfill \\ 1,\hfill & x\ge b\hfill \end{array}\right\}$$

Going from left to right the function increases from 0 to 1. The parameters a and b control the left and right extremes of the sloped portion of the curve.

This block is related to the Z-shaped MF and Pi-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

S MF — Membership value

scalar | vector

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

Parameters

Left point a — Leftmost point of transition area

-3 (default) | scalar

Leftmost point a of the transition area.

Programmatic Use

Block Parameter: a

Type: string, character vector

Default: "-3"

Right point b — Rightmost point of transition area

3 (default) | scalar

Rightmost point b of the transition area.

Programmatic Use

Block Parameter: b

Type: string, character vector

Default: "3"

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