FLIC: fuzzy linear invariant clustering for applications in fuzzy control

We present a new method for fuzzy clustering which is useful for deriving Takagi-Sugeno type rules "if x is A/sub k/, then y=g/sub k/(x)". Unlike the previous works, where the c-means algorithm is used first to form clusters with a single point center and then g/sub k/(x)'s are formed separately for each cluster, we form the clusters and their more general representative g/sub k/(x)'s simultaneously. The rules obtained by our method give 50% smaller error in predicting y from x than that obtained by the previous methods. The clusters obtained by our method are invariant under general linear transformations: translation, rotation, and differential scaling of the coordinates. The clusters obtained by the c-means algorithm are not invariant under differential scaling.<
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