Linguistic Z-number Muirhead mean operators and their applications in ethical-financial portfolio selection

Document Type : Article


1 Department of Industrial Engineering, Science and Research branch, Islamic Azad University, Tehran, Iran.

2 Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran

3 Department of Statistic and Actuarial Science, University of Waterloo, Ontario, Canada.

4 Department of Industrial Engineering, KHATAM University, Tehran, Iran.

5 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran


Traditionally the performance of firms is evaluated by financial criteria, but this study presents a new qualitative comprehensive framework that incorporates the ethical criteria into the portfolio models and it is widely matched with the preferences of socially responsible investors. The increase of corporate deceptions has caused investors or fund managers consider the ethical assessments in their investment management. Therefore, it is essential to develop models that capture the ethical criteria along with the financial criteria in the investment processes. In this study, a multi-stage methodology is proposed and linguistic Z-numbers are applied to represent the evaluation information, and the Muirhead mean (MM) aggregation operators are employed to fuse the input data under linguistic Z-number environment. Hence, we firstly develop four linguistic Z-number Muirhead mean operators. Then, using the max-score rule and the score-accuracy trade-off rule, three qualitative portfolio models are proposed. These models have been aimed to maximize the financial performance of portfolio as main objective and have been distinguished by the ethical goal that the investor follows. The obtained results of numerical example validates the capability of the models for constructing more diversified portfolio based on a trade-off between financial and ethical criteria according to investors’ preferences.