In the spirit of twin parametric-margin support vector machine (TPMSVM) and support vector machine based on fuzzy membership values (FSVM), a new method termed as fuzzy based Lagrangian twin parametric-margin support vector machine (FLTPMSVM) is proposed in this paper to reduce the effect of the outliers. In FLTPMSVM, we assign the weights to each data samples on the basis of fuzzy membership values to reduce the effect of outliers. Also, we consider the square of the 2norm of slack variables

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... make the objective function strongly convex and find the solution of the proposed FLTPMSVM by solving simple linearly convergent iterative schemes instead of solving a pair of quadratic programming problems as in case of SVM, TWSVM, FTSVM and TPMSVM. No need of external toolbox is required for FLTPMSVM. The numerical experiments are performed on artificial as well as well known real-world datasets which show that our proposed FLTPMSVM is having better generalization performance and less training cost in comparison to support vector machine, twin support vector machine, fuzzy twin support vector machine and twin parametric-margin support vector machine. Keywords-Support vector machine; Twin support vector machine; Parametric-margin model; fuzzy membership; Iterative method I.