Proposing DEA-GZBWM Method with Fuzzy Uncertainty

Document Type : Research Paper


1 , Associate Prof., Department of Industrial Management, College of Farabi, University of Tehran, Tehran, Iran.

2 MSc., Department of Industrial Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran.

3 MSc., Department of Industrial Engineering,, Shahabdanesh University, Qom, Iran.

4 MSc., Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran.


Objective: Considering that in most specialized fields, decisions are made in groups, in this study, a method to select the desired option in conditions of uncertainty is presented, which also considers the group decisions to increase the effectiveness.
Methods: In this study, the ZlCWAA method and data envelopment analysis, which are responsible for the averaging of Z numbers and assigning weight to specialists, were used to create the Z number extension of the best-worst method. This method is innovative in decision-making and, in this study, we used the Z number extension of the best-worst group method.
Results: For better decision-making, the information should be more valid, accurate, and reliable. So we compared the FBWM, ZBWM, and DEA-GZBWM methods with each other, based on the case study and data collection from the perspective of each expert on the most important indicators of optimal stock portfolio selection. This comparison showed that the proposed method of DEA-GZBWM has a lower rate of incompatibility than the others. Therefore, the information obtained in this method can be more reliable for us.
Conclusion: To prove the effectiveness of the DEA-GZBWM method, a case study was conducted to show how to use this method in optimal stock portfolio selection; In which the investor, with the help of financial experts (experts in financial markets), invests and selects the optimal stock portfolio from the companies in the stock exchange and securities organization. Then, based on weight, rank, and incompatibility rate, the results of the proposed method, FBWM, and ZBWM methods were compared. This comparison showed that the proposed method is more functional than the others due to its lower incompatibility rate (0.108).


Abadi, F., Sahebi, I., Arab, A., Alavi, A., & Karachi, H. (2018). Application of best-worst method in evaluation of medical tourism development strategy. Decision Science Letters, 7(1), 77–86.
Aboutorab, H., Saberi, M., Asadabadi, M. R., Hussain, O., & Chang, E. (2018). ZBWM: The Z-number extension of Best Worst Method and its application for supplier development. Expert Systems with Applications, 107, 115–125.
Ali, A., & Rashid, T. (2020). Generalized interval-valued trapezoidal fuzzy best-worst multiple criteria decision-making method with applications. Journal of Intelligent & Fuzzy Systems, 38(2), 1705–1719.
Amiri, M., Hashemi-Tabatabaei, M., Ghahremanloo, M., Keshavarz-Ghorabaee, M., Zavadskas, E. K., & Banaitis, A. (2021). A new fuzzy BWM approach for evaluating and selecting a sustainable supplier in supply chain management. International Journal of Sustainable Development & World Ecology, 28(2), 125–142.
Amoozad Mahdiraji, H., Arzaghi, S., Stauskis, G., & Zavadskas, E. K. (2018). A hybrid fuzzy BWM-COPRAS method for analyzing key factors of sustainable architecture. Sustainability, 10(5), 1626.
Charnes, A., Cooper, W. W., & Wei, Q. L. (1987). A Semi-Infinite Multicriteria Programming Approach to Data Envelopment Analysis With Infinitely Many Decision-Making Units.
Cooper, W. W., Seiford, L. M., & Tone, K. (2007). Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software (ج 2). Springer.
de Kaa, G., Scholten, D., Rezaei, J., & Milchram, C. (2017). The battle between battery and fuel cell powered electric vehicles: A BWM approach. Energies, 10(11), 1707.
Dong, Q., & Cooper, O. (2016). A peer-to-peer dynamic adaptive consensus reaching model for the group AHP decision making. European Journal of Operational Research, 250(2), 521–530.
Fahimi, Afshin & Shahbandarzadeh, Hamid (2021). Developing the Markowitz Portfolio Optimization Model Concerning Investor Non - financial Considerations and Supporting Domestic Products. Industrial Management Journal, 13(1), 53-79. (in Persian)
Ghoushchi, S. J., Dorosti, S., Khazaeili, M., & Mardani, A. (2021). Extended approach by using best--worst method on the basis of importance--necessity concept and its application. Applied Intelligence, 1–15.
Guo, S., & Zhao, H. (2017). Fuzzy best-worst multi-criteria decision-making method and its applications. Knowledge-Based Systems, 121, 23–31.
Gupta, H., & Barua, M. K. (2016). Identifying enablers of technological innovation for Indian MSMEs using best--worst multi criteria decision making method. Technological Forecasting and Social Change, 107, 69–79.
Gupta, H., & Barua, M. K. (2017). Supplier selection among SMEs on the basis of their green innovation ability using BWM and fuzzy TOPSIS. Journal of Cleaner Production, 152, 242–258.
Gupta, H., & Barua, M. K. (2018). Modelling cause and effect relationship among enablers of innovation in SMEs. Benchmarking: An International Journal.
Gupta, R. P. (2017). Remote sensing geology. Springer.
Hafezalkotob, A., & Hafezalkotob, A. (2017). A novel approach for combination of individual and group decisions based on fuzzy best-worst method. Applied Soft Computing, 59, 316–325.
Homayounfar, M., Daneshvar, A., Nahavandi, B., & Fallah, F. (2019). Developing a New Classification Method Base d on a Hybrid Machine Learning and Multi Criteria Decision Making Approach. Industrial Management Journal, 11(4), 675-692. (in Persian)
Hussain, A., Chun, J., & Khan, M. (2021). A novel multicriteria decision making (MCDM) approach for precise decision making under a fuzzy environment. Soft Computing, 25(7), 5645–5661.
Maghsoodi, A. I., Mosavat, M., Hafezalkotob, A., & Hafezalkotob, A. (2019). Hybrid hierarchical fuzzy group decision-making based on information axioms and BWM: Prototype design selection. Computers & Industrial Engineering, 127, 788–804.
Mohammadi, M., & Rezaei, J. (2020). Bayesian best-worst method: A probabilistic group decision making model. Omega, 96, 102075.
Rezaei, J. (2015). Best-worst multi-criteria decision-making method. Omega, 53, 49–57.
Rezaei, J. (2016). Best-worst multi-criteria decision-making method: Some properties and a linear model. Omega, 64, 126–130.
Rezaei, J., Nispeling, T., Sarkis, J., & Tavasszy, L. (2016). A supplier selection life cycle approach integrating traditional and environmental criteria using the best worst method. Journal of Cleaner Production, 135, 577–588.
Salimi, N., & Rezaei, J. (2018). Evaluating firms’ R&D performance using best worst method. Evaluation and program planning, 66, 147–155.
Shaverdi, M., Yaghoubi, S., & Soltani, B. (2019). Project Evaluation and Selection in Technology Development Funds with Best-Worst Method (Case Study: Innovation and Prosperity Fund). Industrial Management Journal, 11(3), 461-486. (in Persian)
Tang, J., Yu, S., Liu, F., Chen, X., & Huang, H. (2019). A hierarchical prediction model for lane-changes based on combination of fuzzy C-means and adaptive neural network. Expert systems with applications, 130, 265–275.
Teymouri, E., Amiri, M., Olfat, L., & Zandieh, M. (2020). Presenting a Supplier Selection, Order Allocation, a nd Pricing Model in Multi-item, Single-Period, and Multi-Supplier Supply Chain Management with Surface Re sponse Methodology and Genetic Algorithm Approach. Industrial Management Journal, 12(1), 1-23. (in Persian)
van de Kaa, G., Kamp, L., & Rezaei, J. (2017). Selection of biomass thermochemical conversion technology in the Netherlands: A best worst method approach. Journal of Cleaner Production, 166, 32–39.
Wan, S., Dong, J., & Chen, S.-M. (2021). Fuzzy best-worst method based on generalized interval-valued trapezoidal fuzzy numbers for multi-criteria decision-making. Information Sciences.
Wu, Y., Xu, C., & Zhang, T. (2018). Evaluation of renewable power sources using a fuzzy MCDM based on cumulative prospect theory: A case in China. Energy, 147, 1227–1239.
Xian, S., Chai, J., & Guo, H. (2019). Linguistic-induced ordered weighted averaging operator for multiple attribute group decision-making. International Journal of Intelligent Systems, 34(2), 271–296.
Zadeh, L. A. (2011). The concept of a Z-number-A new direction in uncertain computation. 2011 IEEE International Conference on Information Reuse & Integration, xxii--xxiii.
Zhang, Z., Gao, Y., & Li, Z. (2020). Consensus reaching for social network group decision making by considering leadership and bounded confidence. Knowledge-Based Systems, 204, 106240.