Fuzzy Logic:Centroid Defuzzification

[Rick1138]

Does anyone know how to calculate the centroid of a fuzzy rule set,I am looking for specific formulae for both triangular and Gaussian shaped rules.I've found a lot of explanations on what is being done but no clear explanations on exactly how to do it.Any information would be appreciated.

[Brad]

<img src="graemlins/bugeye.gif" border="0" alt="[Skeptical]" /> ummm....

::whooosh!::
(sound of talk flying way over my head)

[Sinewave]

Yeah I am glad I am not the only one heh.. BTW like the sig starfeelt :D

[Rick1138]

It's not as obscure as it may sound,fuzzy logic deals with sets of which the members may belong to partially,wheras in classical logic members either do or do not belong to a set.In fuzzy logic a grey object can be described as belonging to a certain degree to the set white and a certain degree to the set black.For example,a neutral grey can be defined as belonging 50% to the set black and 50% to the set white.As the grey becomes darker it belongs to a greater degree to the black set and a lesser to the white.The degree to which it belongs to the black and the degree to which it belongs to the white can be represented graphically by a triangle.A Gaussian,or bell-shaped, curve can also be used,but triangles are more common because the calculations are faster to compute.The centroid is just the center of mass of a fuzzy rule,such as the degree to which a certain grey belongs to both black or white,and when a fuzzy set is defuzzified the centroids of all the rules are added together,the problem is that I don't know specifically how to do this,all the literature on the subject I've found tonight is either obscure or self-contradictory.