SDP and SOCP for Outer and Robust Fuzzy Approximation

M. Kumar, R. Stoll, and N. Stoll (Germany)


Fuzzy-modelling, least-squares, Semidefinite Programming, Second-order cone programming, regularization


This study presents the problem of computing minimal size ellipsoid of confidence for the parameters of uncer tain Sugeno type Fuzzy Inference Systems using Semidef inite Programming (SDP) and robust fuzzy approximation with uncertain data using second-order cone programming (SOCP). Sugeno Fuzzy System is linear in Consequent pa rameters but nonlinear in Antecedent parameters. So for the given fixed choice of Antecedent parameters, Semidef inite relaxation techniques developed for uncertain linear equations for computing the intervals of confidence for Consequent parameters and SOCP for computing the ro bust solution to uncertain Consequent parameters, can be directly applied. Also the Antecedent parameters can be identified from uncertain data by solving a regularized non linear least squares approximation problem. Hence an Al gorithm allowing the simultaneous tuning of Antecedent and Consequent parameters and computing the ellipsoid of confidence for Consequent parameters is suggested. Fur ther this ellipsoid can be projected along the Fuzzy out put axis to have outer fuzzy Approximation to uncertain data. Also for robust fuzzy approximation, similar algo rithm based on SOCP is suggested.

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