Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models

Abstract

The construction of interpretable Takagi-Sugeno (TS) fuzzy models by means of clustering is addressed. First, it is shown how the antecedent fuzzy sets and the corresponding consequent parameters of the TS model can be derived from clusters obtained by the Gath-Geva (GG) algorithm. To preserve the partitioning of the antecedent space, linearly transformed input variables can be used in the model. This may, however, complicate the interpretation of the rules. To form an easily interpretable model that does not use the transformed input variables, a new clustering algorithm is proposed, based on the expectation-maximization (EM) identification of Gaussian mixture models. This new technique is applied to two well-known benchmark problems: the MPG (miles per gallon) prediction and a simulated second-order nonlinear process. The obtained results are compared with results from the literature.

Autoregressive time series prediction by means of fuzzy inference systems using nonparametric residual variance estimation

“…The W&M method was found to consistently provide better results than other grid partition based methods, such as the algorithm by Higgins and Goodman [18]. The SC method was found to consistently provide better accuracy than other clustering based identification alternatives using the Gath-Geva [1,15], Gustafson-Kessel [17], hard and fuzzy C-means [13] clustering methods.…”

“…As concrete implementation for this paper we apply the Levenberg-Marquardt second order optimization method [3] for supervised learning, driven by the normalized MSE (NMSE) 1 . A number of supervised learning and optimization methods have been compared for this study, including gradient descent, probabilistic, second order, and conjugate gradient methods.…”

“…First, it produces systems with the lowest number of MFs among the set of alternatives tested. Second, it yields systems almost as accurate as the 1 Normalization is performed against the squared range of the series. most accurate alternative.…”

Fuzzy control turns 50: 10 years later

“…The values of θ i for a particular nonlinear plant could be obtained by identification (either via linear leastsquares if M i were fixed [15], or via non-linear algorithms if M i had to be also identified [16] by adjusting some tunable parameters of the membership functions).…”

Sistema Neuro-Nebuloso para Identificação de Processos de Incineração Multivariáveis Não-Lineares Discretos no Tempo

“…Neste trabalho, um processo de incineração multivariável é representado por um modelo neuro-nebuloso MIMO(Multiple Input Multiple Output), que consiste de um modelo MIMO linear ARX(Auto Regressive with exogenous inputs) com uma estrutura neuronebulosa. O algoritmo Gath-Geva modificado [1] é baseado na identificação da maximização da esperança (EM) de modelos que englobam um número de funções gaussianas. Este tipo de algoritmo de agrupamento pode ser facilmente usado para obter as funções de pertinência da primeira camada intermediária da rede neuro-nebulosa.…”