GAUSSMF

Generates a Gaussian membership function for a given universe. The shape of the Gaussian is defined by two parameters: the center (mean) and the standard deviation (sigma).

The membership value is 1 at the mean and falls off symmetrically according to the standard deviation.

Excel Usage

=GAUSSMF(x, mean, sigma)

x (list[list], required): Array of independent universe variables.
mean (float, required): Gaussian parameter for center (mean) value.
sigma (float, required): Gaussian parameter for standard deviation.

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

Example 1: Gaussian membership over a centered universe

Inputs:

x						mean	sigma
0	1	2	3	4	5	2.5	1

Excel formula:

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

Expected output:

Result
0.0439369
0.324652
0.882497
0.882497
0.324652
0.0439369

Example 2: Gaussian membership at the mean value

Inputs:

x	mean	sigma
1.5	1.5	0.75

Excel formula:

=GAUSSMF(1.5, 1.5, 0.75)

Expected output:

1

Example 3: Gaussian membership with a wide spread

Inputs:

x					mean	sigma
-2	-1	0	1	2	0	2

Excel formula:

=GAUSSMF({-2,-1,0,1,2}, 0, 2)

Expected output:

Result
0.606531
0.882497
1
0.882497
0.606531

Example 4: Gaussian membership centered at a negative mean

Inputs:

x					mean	sigma
-4	-3	-2	-1	0	-2	0.8

Excel formula:

=GAUSSMF({-4,-3,-2,-1,0}, -2, 0.8)

Expected output:

Result
0.0439369
0.457833
1
0.457833
0.0439369

Python Code

Show Code

import numpy as np
from skfuzzy import gaussmf as fuzz_gaussmf

def gaussmf(x, mean, sigma):
    """
    Generate a Gaussian fuzzy membership function.

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

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

    Args:
        x (list[list]): Array of independent universe variables.
        mean (float): Gaussian parameter for center (mean) value.
        sigma (float): Gaussian parameter for standard deviation.

    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"

        if sigma <= 0:
            return "Error: sigma must be positive"

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

Online Calculator

x *

Array of independent universe variables.

mean *

Gaussian parameter for center (mean) value.

sigma *

Gaussian parameter for standard deviation.