A MULTI-OBJECTIVE APPROACH BASED ON MARKOWITZ AND DEA CROSS-EFFICIENCY MODELS FOR THE INTUITIONISTIC FUZZY PORTFOLIO SELECTION PROBLEM

Abstract

Nowadays, investors' main concerns are choosing the best portfolio so that the highest possible investment return 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. Data envelopment analysis (DEA) is also a practical technique that can analyze the efficiency of firms. Few models can address companies' internal performance simultaneously in addition to considering the goals of Markowitz models. Also, we study the return and price fluctuations of assets in the market with the intuitionistic fuzzy numbers for the first time. Therefore, in this paper, we combine all these tools with returns of intuitionistic fuzzy numbers, proposing 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, simultaneously, fully covers all constraints of the Markowitz model. To show the model's practicality, we studied a case study based on information from 50 active enterprises on Tehran Stock Exchange. We solved the proposed model using the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). The obtained results and the comparisons made with the existing approaches show the effectiveness of the proposed model.