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Centre of gravity method (COG)

This approach has its origin in the idea to select a value that, on average, would lead to the smallest error in the sense of a criterion. If is chosen, and the best value is , then the error is . Thus, to determine the least squares method can be used. As weights for each square , one can take the grade of membership with which is a reasonable value. As a result one has to find

(16.4)

Differentiating with respect to the unknown and equating the derivative to zero, the formula

(16.5)

is obtained, which determines the value of the abscissa of the centre of gravity of the area below the membership function .



Next: Centre of singleton method Up: Defuzzification Previous: Defuzzification   Contents
Christian Schmid 2005-05-09