PSIGMF

Generates the product of two sigmoid membership functions. The shape of the curve is defined by multiplying two sigmoids together.

The equation is defined as y = f1(x) * f2(x) where f1 and f2 are sigmoid functions defined by parameters b1, c1 and b2, c2. For a smoothed rect-like function, choose c2 < 0 < c1. For its inverse, choose c1 < 0 < c2.

Excel Usage

=PSIGMF(x, b_one, c_one, b_two, c_two)

x (list[list], required): Array of independent universe variables.
b_one (float, required): Center bias for the first sigmoid.
c_one (float, required): Controls width of the first sigmoidal region.
b_two (float, required): Center bias for the second sigmoid.
c_two (float, required): Controls width of the second sigmoidal region.

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

Example 1: Product of sigmoids forming a smooth window

Inputs:

x								b_one	c_one	b_two	c_two
0	1	2	3	4	5	6	7	2	2	5	-2

Excel formula:

=PSIGMF({0,1,2,3,4,5,6,7}, 2, 2, 5, -2)

Expected output:

Result
0.0179854
0.119163
0.498764
0.864955
0.864955
0.498764
0.119163
0.0179854

Example 2: Product of sigmoids forming an inverse window

Inputs:

x								b_one	c_one	b_two	c_two
0	1	2	3	4	5	6	7	2	-2	5	2

Excel formula:

=PSIGMF({0,1,2,3,4,5,6,7}, 2, -2, 5, 2)

Expected output:

Result
0.0000445813
0.000295375
0.00123631
0.00214401
0.00214401
0.00123631
0.000295375
0.0000445813

Example 3: Product of sigmoids at a scalar midpoint

Inputs:

x	b_one	c_one	b_two	c_two
3.5	2	2	5	-2

Excel formula:

=PSIGMF(3.5, 2, 2, 5, -2)

Expected output:

0.907397

Example 4: Product of sigmoids shifted into a negative domain

Inputs:

x						b_one	c_one	b_two	c_two
-4	-3	-2	-1	0	1	-3	1.5	0	-1.5

Excel formula:

=PSIGMF({-4,-3,-2,-1,0,1}, -3, 1.5, 0, -1.5)

Expected output:

Result
0.181974
0.494507
0.7788
0.7788
0.494507
0.181974

Python Code

Show Code

import numpy as np
from skfuzzy import psigmf as fuzz_psigmf

def psigmf(x, b_one, c_one, b_two, c_two):
    """
    Generate the product of two sigmoid membership functions.

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

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

    Args:
        x (list[list]): Array of independent universe variables.
        b_one (float): Center bias for the first sigmoid.
        c_one (float): Controls width of the first sigmoidal region.
        b_two (float): Center bias for the second sigmoid.
        c_two (float): Controls width of the second sigmoidal region.

    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_psigmf(x_arr, b_one, c_one, b_two, c_two)
        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_one *

Center bias for the first sigmoid.

c_one *

Controls width of the first sigmoidal region.

b_two *

Center bias for the second sigmoid.

c_two *

Controls width of the second sigmoidal region.