# Weighted average method for defuzzification

Weighted average method is one of the simplest and widely used defuzzification technique.

This method is also alternatively called ”**Sugeno defuzzification**” method.

Formed by weighting each functions in the output by its respective maximum membership value

This method is applicable to fuzzy sets with symmetrical output membership functions and yields results that are quite similar to the COA method. This method requires less computational power. The maximum membership value is used to weight each membership function.

Procedure results very close to the COA method

Less computationally intensive

**Note: **The method can be used only for **symmetrical **output membership functions.

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**Example:**

Find defuzzified value for given aggregated fuzzy output set using weighted average method:

The fuzzified value using weighted average defuzzification method is computed as,

As discussed, the center of each symmetric fuzzy output function is multiplied by the height of the function.

x^{*} = ((0.7 × 3) + (1.0 × 7)) / (0.7 + 1.0)

x^{∗} = 5.941