Pi-shaped MF

Pi-shaped membership function

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Libraries:
Fuzzy Logic Toolbox / Membership Functions

Description

The Pi-shaped MF block implements a pi-shaped membership function.

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

The parameters a and d control the left and right base points or feet of the curve. The parameters b and c control the left and right top points or shoulders of the curve.

This block is related to the Z-shaped MF and 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

Pi MF — Membership value

scalar | vector

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

Parameters

Left base point a — Foot of left transition area

-9 (default) | scalar

Foot a of the left transition area.

Programmatic Use

Block Parameter: a

Type: string, character vector

Default: "-9"

Left top point b — Shoulder of left transition area

-7 (default) | scalar

Shoulder b of the left transition area.

Programmatic Use

Block Parameter: b

Type: string, character vector

Default: "-7"

Right top point c — Shoulder of right transition area

-9 (default) | scalar

Shoulder c of the right transition area.

Programmatic Use

Block Parameter: c

Type: string, character vector

Default: "2"

Right base point d — Foot of right transition area

-7 (default) | scalar

Foot d of the right transition area.

Programmatic Use

Block Parameter: d

Type: string, character vector

Default: "8"

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