DEFUZZ

Defuzzification converts a fuzzy membership function into a single boolean or crisp numerical value. It is the final step in a fuzzy logic control system.

This function takes an array of universe variables and their corresponding fuzzy membership values, and applies a selected defuzzification method such as the centroid of area.

Excel Usage

=DEFUZZ(x, mfx, defuzz_mode)

x (list[list], required): Array of independent universe variables.
mfx (list[list], required): Array of fuzzy membership values corresponding to x.
defuzz_mode (str, optional, default: “centroid”): Defuzzification method to use.

Returns (float): Defuzzified crisp result.

Example 1: Centroid defuzzification of a simple triangle

Inputs:

x			mfx			defuzz_mode
0	1	2	0	1	0	centroid

Excel formula:

=DEFUZZ({0,1,2}, {0,1,0}, "centroid")

Expected output:

1

Example 2: Bisector defuzzification of a symmetric triangle

Inputs:

x			mfx			defuzz_mode
0	1	2	0	1	0	bisector

Excel formula:

=DEFUZZ({0,1,2}, {0,1,0}, "bisector")

Expected output:

1

Example 3: Mean of maximum on a flat peak

Inputs:

x				mfx				defuzz_mode
0	1	2	3	0	1	1	0	mom

Excel formula:

=DEFUZZ({0,1,2,3}, {0,1,1,0}, "mom")

Expected output:

1.5

Example 4: Largest of maximum on repeated peaks

Inputs:

x				mfx				defuzz_mode
0	1	2	3	0.2	0.7	0.7	0.1	lom

Excel formula:

=DEFUZZ({0,1,2,3}, {0.2,0.7,0.7,0.1}, "lom")

Expected output:

2

Python Code

Show Code

import numpy as np
from skfuzzy import defuzz as fuzz_defuzz

def defuzz(x, mfx, defuzz_mode='centroid'):
    """
    Defuzzify a membership function to return a crisp value.

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

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

    Args:
        x (list[list]): Array of independent universe variables.
        mfx (list[list]): Array of fuzzy membership values corresponding to x.
        defuzz_mode (str, optional): Defuzzification method to use. Valid options: Centroid, Bisector, Mean of Maximum, Min of Maximum, Max of Maximum. Default is 'centroid'.

    Returns:
        float: Defuzzified crisp result.
    """
    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)
        mfx_arr = to1d(mfx)

        if len(x_arr) == 0 or len(mfx_arr) == 0:
            return "Error: Input arrays cannot be empty"

        if len(x_arr) != len(mfx_arr):
            return "Error: x and mfx must have the same number of elements"

        result = fuzz_defuzz(x_arr, mfx_arr, mode=defuzz_mode)
        return float(result)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

x *

Array of independent universe variables.

mfx *

Array of fuzzy membership values corresponding to x.

defuzz_mode

Defuzzification method to use.