SIGMF

Generates a basic sigmoid membership function. The shape of the sigmoid is defined by its center point and width.

The equation for the sigmoid function is: y = 1 / (1. + exp[- c * (x - b)]). With c > 0, the left side approaches 0 and right side approaches 1. With c < 0, the opposite is true.

Excel Usage

=SIGMF(x, b, c)

• x (list[list], required): Array of independent universe variables.
• b (float, required): Offset or bias. This is the center value of the sigmoid, where it equals 0.5.
• c (float, required): Controls width of the sigmoidal region (magnitude) and which side is open (sign).

Returns (list[list]): Array of membership values corresponding to the input universe.

Example 1: Increasing sigmoid membership profile

Inputs:

x						b	c
0	1	2	3	4	5	2.5	1

Excel formula:

=SIGMF({0,1,2,3,4,5}, 2.5, 1)

Expected output:

Result
0.0758582
0.182426
0.377541
0.622459
0.817574
0.924142

Example 2: Decreasing sigmoid membership profile

Inputs:

x						b	c
0	1	2	3	4	5	2.5	-1

Excel formula:

=SIGMF({0,1,2,3,4,5}, 2.5, -1)

Expected output:

Result
0.924142
0.817574
0.622459
0.377541
0.182426
0.0758582

Example 3: Sigmoid membership at its midpoint

Inputs:

x	b	c
2.5	2.5	3

Excel formula:

=SIGMF(2.5, 2.5, 3)

Expected output:

0.5

Example 4: Sigmoid membership with a shallow slope

Inputs:

x					b	c
-2	-1	0	1	2	0	0.5

Excel formula:

=SIGMF({-2,-1,0,1,2}, 0, 0.5)

Expected output:

Result
0.268941
0.377541
0.5
0.622459
0.731059

Python Code

Show Code

import numpy as np
from skfuzzy import sigmf as fuzz_sigmf

def sigmf(x, b, c):
    """
    Generate a basic sigmoid membership function.

    See: https://pythonhosted.org/scikit-fuzzy/api/skfuzzy.html#skfuzzy.sigmf

    This example function is provided as-is without any representation of accuracy.

    Args:
        x (list[list]): Array of independent universe variables.
        b (float): Offset or bias. This is the center value of the sigmoid, where it equals 0.5.
        c (float): Controls width of the sigmoidal region (magnitude) and which side is open (sign).

    Returns:
        list[list]: Array of membership values corresponding to the input universe.
    """
    try:
        def to1d(arr):
            if isinstance(arr, list):
                flat = []
                for row in arr:
                    row_list = row if isinstance(row, list) else [row]
                    for val in row_list:
                        try:
                            flat.append(float(val))
                        except (TypeError, ValueError):
                            continue
                return np.array(flat)
            return np.array([float(arr)])

        x_arr = to1d(x)
        if len(x_arr) == 0:
            return "Error: Input mapping array x cannot be empty"

        result = fuzz_sigmf(x_arr, b, c)
        return [[float(val)] for val in result]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

x *

Array of independent universe variables.

b *

Offset or bias. This is the center value of the sigmoid, where it equals 0.5.

c *

Controls width of the sigmoidal region (magnitude) and which side is open (sign).