# CenterOfGravity.java

```package libai.fuzzy.defuzzifiers;

import java.awt.*;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;

/**
* Defuzzifier method that calculates the center of gravity of given function.
* Formally the center of gravity is Integral(x.f(x)) / Integral(f(x)) for the
* whole interval. This implementation uses Riemann's sums to calculate the
* integrals of both functions.
*
* @author kronenthaler
*/
public class CenterOfGravity extends Defuzzifier {

/**
* Implements the center of gravity by calculating the Riemann's sums of the
* area using the trapezoidal rule. It assumes the x points are equally
* spaced across the whole domain of the function.
*
* @param function the list of points [x, f(x)] representing the function to
* analyze.
* @return the center of gravity of the function.
*
*/
@Override
public double getValue(List<Point.Double> function) {
Collections.sort(function, new Comparator<Point.Double>() {
@Override
public int compare(Point.Double o1, Point.Double o2) {
return (int) (o1.x - o2.x);
}
});

double denominator = riemmanSum(function);

// copy the points but applying th x.f(x)
List<Point.Double> xFunction = new ArrayList<>();
for (Point.Double point : function) {
}
double nominator = riemmanSum(xFunction);

return nominator / denominator;
}

protected double riemmanSum(List<Point.Double> function) {
return riemmanSum(function, function.get(function.size() - 1).x);
}

protected double riemmanSum(List<Point.Double> function, double maxX) {
double result = 0;
for (int i = 0; i < function.size() - 1; i++) {
Point.Double point = function.get(i);
Point.Double point1 = function.get(i + 1);
double delta = point1.x - point.x;

if (point.x < maxX && point1.x > maxX) {
double t = (maxX - point.x) / delta;
double y = point.y + (t * delta);
result += ((point.y + y) / 2.) * Math.abs(maxX - point.x);
break;
}

result += ((point.y + point1.y) / 2.) * delta;
}
return result;
}

@Override
public String toString() {
return "COG";
}
}
```