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

aggregated fuzzy output
Aggregated fuzzy output

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.

weighted average method equation

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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weighted average method

Example:

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

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


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