Fuzzy Optimization and Decision Making

, Volume 3, Issue 1, pp 63–82 | Cite as

Robust Solution to Fuzzy Identification Problem with Uncertain Data by Regularization

  • Mohit Kumar
  • Regina Stoll
  • Norbert Stoll


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.

fuzzy-modelling least-squares problems uncertainty robustness second-order cone programming regularization robust identification 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Mohit Kumar
    • 1
  • Regina Stoll
    • 1
  • Norbert Stoll
    • 2
  1. 1.Institute of Occupational and Social Medicine, Faculty of MedicineUniversity of RostockRostockGermany
  2. 2.Institute of Automation, Department of Electrical Engineering and Information TechnologyUniversity of RostockRostock-WarnemündeGermany

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