What is Center of Sums and Center of Largest Area

Center of Sums :-

Center of sums is the fastest defuzzification method. This process involves the algebraic sum of individual output fuzzy sets. The only drawback of this method is that intersecting areas are added twice. The algebraic equation for defuzzified value is given by the equation:

Algebraic equation for defuzzified value

The center of sums weights are the areas of the respective membership functions. Whereas in a weighted average, weights are individual membership values.

Center of Largest Area :-

If the output fuzzy set has two convex sub-regions, then the center of gravity of the convex fuzzy sub-region with largest area is used to obtain the defuzzified value of the output.
The algebraic equation for the defuzzified value in this case is given by

equation-for-defuzzified-value-of-output

where,

this corresponds to that of largest area

corresponds to that of largest area.

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