An overview of portfolio optimization using fuzzy data envelopment analysis models

Document Type: Review Paper


Department of Industrial Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran.



A combination of projects, assets, programs, and other components put together in a set is called a portfolio. Arranging these components helps to facilitate the efficient management of the set and subsequently leads to achieving the strategic goals. Generally, the components of the portfolio are quantifiable and measurable which makes it possible for management to manage, prioritize, and measure different portfolios. In recent years, the portfolio in various sectors of economics, management, industry, and especially project management has been widely applied and numerous researches have been done based on mathematical models to choose the best portfolio. Among the various mathematical models, the application of data envelopment analysis models due to the unique features as well as the capability of ranking and evaluating performances has been taken by some researchers into account. In this regard, several articles have been written on selecting the best portfolio in various fields, including selecting the best stocks portfolio, selecting the best projects, portfolio of manufactured products, portfolio of patents, selecting the portfolio of assets and liabilities, etc. After presenting the Markowitz mean-variance model for portfolio optimization, these pieces of research have witnessed significant changes. Moreover, after the presentation of the fuzzy set theory by Professor Lotfizadeh, despite the ambiguities in the selection of multiple portfolios, a wide range of applications in portfolio optimization was created by combining mathematical models of portfolio optimization.


Main Subjects

[1]     Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science30(9), 1078-1092.
[2]     Zadeh, L. A. (1965). Fuzzy sets. Information and control8(3), 338-353.
[3]     Atanassov, K. (2016). Intuitionistic fuzzy sets. International Journal Bioautomation20, 1.
[4]     Edalatpanah, S. A. (2019). A data envelopment analysis model with triangular intuitionistic fuzzy numbers. International journal of data envelopment analysis7(4), 47-58.
[5]     Charnes, A., & Cooper, W. W. (1984). Preface to topics in data envelopment analysis. Annals of operations research2(1), 59-94.
[6]     Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research2(6), 429-444.
[7]     Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the royal statistical society: series A (General)120(3), 253-281.
[8]     Edalatpanah, S. A. (2018). Neutrosophic perspective on DEA. Journal of applied research on industrial engineering5(4), 339-345.
[9]     Mashayekhi, Z., & Omrani, H. (2016). An integrated multi-objective Markowitz–DEA cross-efficiency model with fuzzy returns for portfolio selection problem. Applied soft computing38, 1-9.
[10] Chen, W., Gai, Y., & Gupta, P. (2018). Efficiency evaluation of fuzzy portfolio in different risk measures via DEA. Annals of operations research269(1-2), 103-127.
[11] Tavana, M., Keramatpour, M., Santos-Arteaga, F. J., & Ghorbaniane, E. (2015). A fuzzy hybrid project portfolio selection method using data envelopment analysis, TOPSIS and integer programming. Expert systems with applications42(22), 8432-8444.
[12] Cooper, W. W., Seiford, L. M., & Tone, K. (2001). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software. Journal-operational research society52(12), 1408-1409.
[13] Najafi, H. S., & Edalatpanah, S. A. (2013). An improved model for iterative algorithms in fuzzy linear systems. Computational mathematics and modeling24(3), 443-451.
[14] Edalatpanah, S. A. (2020). Data envelopment analysis based on triangular neutrosophic numbers. CAAI transactions on intelligence technology. DOI: 10.1049/trit.2020.0016.
[15] Chen, W., Li, S. S., Zhang, J., & Mehlawat, M. K. (2020). A comprehensive model for fuzzy multi-objective portfolio selection based on DEA cross-efficiency model. Soft computing24(4), 2515-2526.
[16] Edirisinghe, N. C., & Zhang, X. (2007). Generalized DEA model of fundamental analysis and its application to portfolio optimization. Journal of banking & finance31(11), 3311-3335.
[17] Mehlawat, M. K., Kumar, A., Yadav, S., & Chen, W. (2018). Data envelopment analysis based fuzzy multi-objective portfolio selection model involving higher moments. Information sciences460, 128-150.
[18] Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science30(9), 1078-1092.