fuzzy membership function

This study introduces a novel approach integrating a support vector machine (SVM) with an optimal portfolio construction model. Leveraging the Radial Basis Function (RBF) kernel, the SVM identifies assets with higher growth potential. However, due to inherent uncertainties, some input points may not be precisely classified into their respective classes in various applications. To mitigate the influence of noise, a new fuzzy support vector machine (NFSVM) is employed to select assets. Here, each sample point is assigned a membership value using a fuzzy membership function, as documented in existing literature [1]. Additionally, the SVM model incorporates principal component analysis (PCA)to eliminate correlated technical indicators. Further, Markowitz’s mean-variance model (MV model) with cardinality constraints and without cardinality constraints is employed for the assets selected by SVM, FSVM, and NFSVM for optimal portfolio construction.The performance of the proposed model is experimentally assessed using a data set derived from the Nifty 50 and Euro Stoxx 50 index. The experimental results demonstrate that the optimal portfolio obtained from the NFSVM with the Markowitz mean-variance model outperforms the one generated by the SVM. This outcome substantiates the effectiveness and efficiency of the proposed model as an advanced approach for optimizing investment portfolios.

This paper considers a biobjective transportation problem with various fuzzy objective functions coefficients. Fuzzy coefficients can be of different types such as triangular, trapezoidal, (semi) $L-R$, or flat (semi) $L-R$ fuzzy numbers. First, we convert the problem to a parametric interval biobjective transportation problem using $gamma$-cuts of fuzzy coefficients. Then, we consider a fix $gamma$-cut and obtain a necessarily weak efficient solution to the yielded interval biobjective program by a new algorithm. It uses basic feasible solutions and the parametric simplex algorithm. Furthermore, we suggest another algorithm for finding a reasonable solution, called $gamma^*$-necessarily weak efficient, to the main biobjective transportation problem. To illustrate the validity and performance of the proposed algorithms, we present some numerical examples.

Fuzzification of support vector machine has been utilized to deal with outlier and noise problem. This importance is achieved, by the means of fuzzy membership function, which is generally built based on the distance of the points to the class centroid. The focus of this research is twofold. Firstly, by taking the advantage of robust statistics in the fuzzy SVM, more emphasis on reducing the impact of outliers on the generalizability of SVM has been placed. Moreover, the variety of membership function for the elliptical data has been designated, based on the classic and robust Mahalanobis distance. Minimum covariance determinant and orthogonalised Gnanadesikan Kettenring estimators are employed in the structure of the robust--fuzzy SVM.By implementing the new membership function, the disadvantages of the traditional fuzzy membership function has been rectified. Simulated and real benchmarking data set confirm the effectiveness of the proposed methods. Compared with the traditional SVM and fuzzy SVM, these methods give a better performance on reducing the effects of outliers and significantly improves the classification accuracy and generalization.