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_k, then y=g _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_k(x)´s are formed separately for each cluster, we form the clusters and their more general representative g_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