In this paper an on-line fuzzy identification of Takagi Sugeno fuzzy model is presented. The presented method combines a recursive Gustafson–Kessel clustering algorithm and the fuzzy recursive least squares method. The on-line Gustafson–Kessel clustering method is derived. The recursive equations for fuzzy covariance matrix, its inverse and cluster centers are given. The use of the method is pr...

In this paper one presents a new fuzzy clustering algorithm based on a dissimilarity function determined by three parameters. This algorithm can be considered a generalization of the Gustafson-Kessel algorithm for fuzzy clustering.

The Gustafson-Kessel fuzzy clustering algorithm is capable of detecting hyperellipsoidal clusters of different sizes and orientations by adjusting the covariance matrix of data, thus overcoming the drawbacks of conventional fuzzy c-means algorithm. In this paper, an adaptive version of the Gustafson-Kessel algorithm is proposed. The way to adjust the covariance matrix iteratively is introduced ...

We extend expansion formulas of Liu given in 2013 to the context multiple series over root systems. and others have shown usefulness these Special Functions number-theoretic contexts. Wang Ma's generalizations Liu's work which they obtained using q-Lagrange inversion. use An Cn Bailey transformation other summation theorems due Gustafson, Milne, Milne Lilly, others, from theory An, Dn basic hyp...

In this paper, we propose a Context-based Gustafson-Kessel (CGK) clustering that builds Information Granulation (IG) in the form of fuzzy set. The fundamental idea of this clustering is based on Conditional Fuzzy C-Means (CFCM) clustering introduced by Pedrycz. The proposed clustering develops clusters preserving homogeneity of the clustered patterns associated with the input and output space. ...

The inverted pendulum is a highly nonlinear and open loop unstable system. To develop an accurate model of the inverted pendulum, different linear and nonlinear methods of identification will be used. However one of the problems encountered during modeling is the collection of experimental data from the inverted pendulum system. Since the output data from the unstable system does not show enoug...

Many researchers in the field of forensic odontology have questioned the error estimates stated in Gustafson's paper outlining the relationship between certain dental attributes and age. In a substantial re-working of Gustafson's data, Maples and Rice corrected Gustafson's regression statistics and found that the error associated with the age estimate was nearly double that claimed by Gustafson...