Matrix computations (3rd ed.)
Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
Parameter Estimation in the Presence of Bounded Data Uncertainties
SIAM Journal on Matrix Analysis and Applications
Rule-based modeling: precision and transparency
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Constructing fuzzy models with linguistic integrity from numerical data-AFRELI algorithm
IEEE Transactions on Fuzzy Systems
On the estimation of parameters of Takagi-Sugeno fuzzy filte
IEEE Transactions on Fuzzy Systems
Adaptive fuzzy filtering in a deterministic setting
IEEE Transactions on Fuzzy Systems
Variational bayes for a mixed stochastic/deterministic fuzzy filter
IEEE Transactions on Fuzzy Systems
A mixture of fuzzy filters applied to the analysis of heartbeat intervals
Fuzzy Optimization and Decision Making
An energy-gain bounding approach to robust fuzzy identification
Automatica (Journal of IFAC)
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This study considers the robust identification of the parameters describing a Sugeno type fuzzy inference system with uncertain data. The objective is to minimize the worst-case residual error using a numerically efficient algorithm. The Sugeno type fuzzy systems are linear in consequent parameters but nonlinear in antecedent parameters. The robust consequent parameters identification problem can be formulated as second-order cone programming problem. The optimal solution of this second-order cone problem can be interpreted as solution of a Tikhonov regularization problem with a special choice of regularization parameter which is optimal for robustness (Ghaoui and Lebret (1997). SAIM Journal of Matrix Analysis and Applications 18, 1035–1064). The final regularized nonlinear optimization problem allowing simultaneous identification of antecedent and consequent parameters is solved iteratively using a generalized Gauss–Newton like method. To illustrate the approach, several simulation studies on numerical examples including the modelling of a spectral data function (one-dimensional benchmark example) is provided. The proposed robust fuzzy identification scheme has been applied to approximate the physical fitness of patients with a fuzzy expert system. The identified fuzzy expert system is shown to be capable of capturing the decisions (experiences) of a medical expert.