Novel linear programming models based on distance measure of IFSs and modified TOPSIS method for portfolio selection

Abstract

Due to the unavailability of time series data for newly listed stocks or products, it is a challenge for investors to make rational portfolio selection under uncertain circumstances. To solve the problem, a new approach is put forward in this paper. Firstly, the problem is considered as a multi-criteria decision making (MCDM) problem based on the assumption that the assessments are given in intuitionistic fuzzy set (IFS) form, which can better describe the uncertainty. Then, the TOPSIS method, which is widely used in MCDM problem, has been modified in two aspects. On the one hand, the new definitions of Absolute Positive Ideal Solution (APIS) and Absolute Negative Ideal Solution (ANIS) are proposed to represent the best returns and the greatest cost/risk in portfolio selection. They are more meaningful than the definitions of Positive Ideal Solution (PIS) and Negative Ideal Solution (NIS), which could only express the best and the worst case of portfolio but cannot achieve a balance between returns and risk. On the other hand, the weighted closeness coefficient is refined to offer the more appropriate results that are consistent with investors’ demands or preferences. In addition, based on distance measure of IFSs, several novel linear programming models with different constraints are proposed to allocate the investment ratios according to investors’ demands. The models can make up for the disadvantage of TOPSIS method which only considers the ranking of investments but neglects the investment ratios. Finally, compared with the conventional TOPSIS method and the IF ELECTRE Method in a numerical example, our new approach is demonstrated to be more effective and more flexible. Particularly, it can provide a more appropriate strategy in accordance with investors’ preferences and demands.