I'm doing fuzzy logic and I need to use the center of sums method to calculate a value.
I have the graph of functions here:
Sorry for the low quality, but I think this suffices.
The formula is with regards to the center of sums is $\frac{\sum_{i=1}^n A_1x_1}{\sum_{i=1}^n A_1}$
Where $A_i$ are the areas and $x_i$ are the x coordinates of the centroids/geometric centers of the areas.
Now, let's just observe the trapezoid to the left (i.e. the one where $x \in (0, 0.5)$. I'm having trouble determining the geometric centre for the trapezoid to the left. I know that for a symmetric figure (i.e. a rectangle), the geometric center would be in the middle of its x span. However, since my trapezoid isn't symmetric, I have trouble finding it.
Could someone help?