A multi-objective approach based on Markowitz and DEA cross-efficiency models for the intuitionistic fuzzy portfolio selection problem

Abstract

Nowadays, the main concerns of investors are choosing the best portfolio in a way that the highest possible return of investment can be achieved by accepting the least risk. In this regard, the classical Markowitz model is one of the most widely used models which helps investors get closer to their goals. On the other hand, data envelopment analysis (DEA) is also a practical technique that can analyze the efficiency of enterprises. However, in real problems, we have faced with several uncertainty issues and the intuitionistic fuzzy set (IFS) is one of the best tools to handle these phenomena. Therefore, in this paper, we combine all these tools and with returns of intuitionistic fuzzy numbers, propose a new combined Markowitz and the cross DEA models. Furthermore, to get the best portfolio of assets, this model obtains the efficiency of all companies and at the same time, fully covers all constraints of the Markowitz model. To show the practicality of the model, we studied a case study based on information of 50 active enterprises in the Tehran Stock Exchange and solved the proposed model using the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). The obtained results as well as the comparisons made with the existing approaches show the effectiveness of the proposed model.