Ranking of Efficient Fuzzy Portfolios by Hybrid MSBM-TOPSIS Technique

• Autorzy: Aggarwal Abha , Gupta Anjana , Verma Rajkumar , Kumari Reenu

Identyfikatory

DOI

10.2478/fcds-2025-0001

• Języki publikacji: EN

Abstrakty

EN

This study focuses on ranking of investment portfolios by integrating the Modified Slack Based Measure (MSBM) of Data Envelopment Analysis (DEA) with a multi-criteria decision-making method. Specifically, it extends the MSBM model to evaluate portfolios with positive and negative inputs and outputs in a fuzzy environment using possibilistic mean return of the assets as output and possibilistic variance and semi-variance as inputs. The ranking process involves two stages: first, portfolios are evaluated using an MSBM fuzzy portfolio model, followed by their ranking through the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method. This hybrid MSBM-TOPSIS approach provides a robust and reliable ranking system, enabling investors to identify efficient portfolios by leveraging the strengths of both methods. Detailed numerical illustrations are presented here to authenticate the proposed approach and the obtained results are compared with other existing DEA methods that validate the accuracy and feasibility of the proposed technique.

Słowa kluczowe

EN

fuzzy set; Modified Slack Based Measure; data envelopment analysis; portfolio; TOPSIS method

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2025
• Tom: Vol. 50, No. 1
• Strony: 3--26
• Opis fizyczny: Bibliogr. 48 poz., rys., tab.

Twórcy

autor

Aggarwal Abha

• Faculty of University School of Basic and Applied Sciences, GGSIP University, Delhi, India

autor

Gupta Anjana

• Faculty of Department of Applied Mathematics, Delhi Technological University, Delhi, India

autor

Verma Rajkumar

• Department of Management Control and Information Systems, University of Chile, Santigo, Chile and Guest faculty at Indira Gandhi Delhi Technological University for Woman, Delhi, India

autor

Kumari Reenu

• Faculty of Applied Science Department, Maharaja Surajmal Institute of Technology, and research scholar in Department of Applied Mathematics, Delhi Technological University, Delhi, India

Bibliografia

• [1] A. Aldamak and S. Zolfaghari. Review of efficiency ranking methods in data envelopment analysis. Measurement, 106: 161-172, 2017.
• [2] P. Andersen and N. C. Petersen. A procedure for ranking efficient units in data envelopment analysis. Management science, 39(10): 1261-1264, 1993.
• [3] B. Arabi, M. Toloo, Z. Yang, P. Zhang, and B. Xu. Sustainable refrigeration technology selection: An innovative dea-topsis hybrid model. Environmental Science & Policy, 158: 103780, 2024.
• [4] S. A. Banihashemi and M. Khalilzadeh. A new approach for ranking efficient DMUs with data envelopment analysis. World Journal of Engineering, 17(4): 573-583, 2020.
• [5] R. D. Banker, A. Charnes, and W. W. Cooper. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9): 1078-1092, 1984.
• [6] P. Bansal and A. Mehra. Integrated dynamic interval data envelopment analysis in the presence of integer and negative data. Journal of Industrial and Management Optimization, 18(2): 1339-1363, 2022.
• [7] C. Carlsson and R. Fullér. On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems, 122(2): 315-326, 2001.
• [8] C. Carlsson, R. Fullér, and P. Majlender. A possibilistic approach to selecting portfolios with highest utility score. Fuzzy sets and systems, 131(1): 13-21, 2002.
• [9] A. Charnes, W. W. Cooper, and E. Rhodes. Measuring the efficiency of decision making units. European journal of operational research, 2(6): 429-444, 1978.
• [10] W. Chen. Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem. Physica A: Statistical Mechanics and its Applications, 429: 125-139, 2015.
• [11] W. Chen, Y. Gai, and P. Gupta. Efficiency evaluation of fuzzy portfolio in di erent risk measures via DEA. Annals of Operations Research, 269(1): 103-127, 2018.
• [12] G. Cheng, P. Zervopoulos, and Z. Qian. A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis. European Journal of Operational Research, 225(1): 100-105, 2013.
• [13] A. Chitnis and O. S. Vaidya. Efficiency ranking method using DEA and topsis (erm-dt): case of an indian bank. Benchmarking: An International Journal, 2016.
• [14] H. Ding, Z. Zhou, H. Xiao, C. Ma, and W. Liu. Performance evaluation of portfolios with margin requirements. Mathematical Problems in Engineering, 2014, 2014.
• [15] A. Emrouznejad, A. L. Anouze, and E. Thanassoulis. A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using dea. European Journal of Operational Research, 200(1): 297-304, 2010.
• [16] Y. Ersoy. Performance evaluation in distance education by using data envelopment analysis (dea) and topsis methods. Arabian Journal for Science and Engineering, 46(2): 1803-1817, 2021.
• [17] P. Gupta, M. K. Mehlawat, A. Kumar, S. Yadav, and A. Aggarwal. A credibilistic fuzzy dea approach for portfolio efficiency evaluation and rebalancing toward benchmark portfolios using positive and negative returns. International Journal of Fuzzy Systems, 22(3): 824-843, 2020.
• [18] A. Hadi-Vencheh and A. Esmaeilzadeh. A new super-efficiency model in the presence of negative data. Journal of the Operational Research Society, 64(3): 396-401, 2013.
• [19] A. Hatami-Marbini, J. Pourmahmoud, and E. Babazadeh. A modified superefficiency in the range directional model. Computers & Industrial Engineering, 120: 442-449, 2018.
• [20] C.-L. Hwang and K. Yoon. Methods for multiple attribute decision making. In Multiple attribute decision making, pages 58-191. Springer, 1981.
• [21] J. Jablonsky. Multicriteria approaches for ranking of efficient units in DEA models. Central European Journal of Operations Research, 20(3): 435-449, 2012.
• [22] R. Lin. Cross-efficiency evaluation capable of dealing with negative data: A directional distance function based approach. Journal of the Operational Research Society, 71(3):505-516, 2020.
• [23] R. Lin and Z. Chen. A directional distance based super-efficiency dea model handling negative data. Journal of the operational Research Society, 68(11): 1312-1322, 2017.
• [24] W. Liu, Z. Zhou, D. Liu, and H. Xiao. Estimation of portfolio efficiency via dea. Omega, 52: 107-118, 2015.
• [25] Y. J. Liu and W. G. Zhang. Fuzzy portfolio optimization model under real constraints. Insurance: Mathematics and Economics, 53(3): 704-711, 2013.
• [26] F. H. Lotfi, R. Fallahnejad, and N. Navidi. Ranking efficient units in DEA by using TOPSIS method. Applied Mathematical Sciences, 5(17): 805-815, 2011.
• [27] H. M. Markowitz. Portfolio selection. Yale university press, 1968.
• [28] Z. Mashayekhi and H. Omrani. An integrated multi-objective markowitz-DEA cross-efficiency model with fuzzy returns for portfolio selection problem. Applied Soft Computing, 38: 1-9, 2016.
• [29] M. K. Mehlawat, P. Gupta, A. Kumar, S. Yadav, and A. Aggarwal. Multiobjective fuzzy portfolio performance evaluation using data envelopment analysis under credibilistic framework. IEEE Transactions on Fuzzy Systems, 28(11): 2726-2737, 2020.
• [30] N. R. Mohd Rashid, B. A. Halim, N. S. Tarmizi, N. F. S. Faizal, and I. Zulkeflee. Efficiency measurement and ranking of malaysian water supply service using hybrid dea-topsis. In AIP Conference Proceedings, volume 2905. AIP Publishing, 2024.
• [31] H. Omrani, M. Shamsi, and A. Emrouznejad. Evaluating sustainable efficiency of decision-making units considering undesirable outputs: an application to airline using integrated multi-objective dea-topsis. Environment, Development and Sustainability, pages 1-32, 2022.
• [32] Z. Pan, Y. Wang, Y. Zhou, and Y. Wang. Analysis of the water use efficiency using super-efficiency data envelopment analysis. Applied Water Science, 10(6): 1-11, 2020.
• [33] M. Portela, E. Thanassoulis, and G. Simpson. A directional distance approach to deal with negative data in DEA: An application to bank branches. Journal of Operational Research Society, 55(10): 1111-1121, 2004.
• [34] S. A. Rakhshan. Efficiency ranking of decision making units in data envelopment analysis by using TOPSIS-DEA method. Journal of the Operational Research Society, 68(8): 906-918, 2017.
• [35] K. Rashidi and K. Cullinane. A comparison of fuzzy dea and fuzzy topsis in sustainable supplier selection: Implications for sourcing strategy. Expert Systems with Applications, 121: 266-281, 2019.
• [36] A. Saeidifar and E. Pasha. The possibilistic moments of fuzzy numbers and their applications. Journal of computational and applied mathematics, 223(2): 1028-1042, 2009.
• [37] J. A. Sharp, W. Meng, and W. Liu. A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs. Journal of the Operational Research Society, 58(12): 1672-1677, 2007.
• [38] M. Soltanifar, M. Tavana, F. J. Santos-Arteaga, and H. Sharafi. A hybrid multi-attribute decision-making and data envelopment analysis model with heterogeneous attributes: The case of sustainable development goals. Environmental Science & Policy, 147: 89-102, 2023.
• [39] K. Tone, T.-S. Chang, and C.-H. Wu. Handling negative data in slacks-based measure data envelopment analysis models. European Journal of Operational Research, 282(3): 926-935, 2020.
• [40] T. H. Tran, Y. Mao, P. Nathanail, P.-O. Siebers, and D. Robinson. Integrating slacks-based measure of efficiency and super-efficiency in data envelopment analysis. Omega, 85: 156-165, 2019.
• [41] E. Vercher and J. D. Bermúdez. Portfolio optimization using a credibility mean-absolute semi-deviation model. Expert Systems with Applications, 42(20): 7121-7131, 2015.
• [42] F. Wei, J. Song, C. Jiao, and F. Yang. A modified slacks-based ranking method handling negative data in data envelopment analysis. Expert Systems, 36(1): e12329, 2019.
• [43] H. Xiao, T. Ren, and T. Ren. Estimation of fuzzy portfolio efficiency via an improved DEA approach. INFOR: Information Systems and Operational Research, 58(3): 478-510, 2020.
• [44] L. A. Zadeh. Fuzzy set theory and its applications. University of California, California, 8: 338, 1965.
• [45] L. A. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy sets and systems, 1(1): 3-28, 1978.
• [46] W.-G. Zhang and Z.-K. Nie. On possibilistic variance of fuzzy numbers. In International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing, pages 398-402. Springer, 2003.
• [47] X.-X. Zhang, W. Liu, X. Wang, W. Zuo, Y.-M. Wang, and L. Sun. Ranking dmus by using interval efficiencies in data envelopment analysis. Journal of Intelligent & Fuzzy Systems, (Preprint): 1-13, 2024.
• [48] Z. Zhou, Q. Jin, H. Xiao, Q. Wu, and W. Liu. Estimation of cardinality constrained portfolio efficiency via segmented dea. Omega, 76 :28-37, 2018.