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

Traditionally, the performance of firms is evaluated based on financial criteria; however, the present study aims to propose a new qualitative comprehensive framework that incorporates ethical criteria into the portfolio models and is widely matched with the preferences of socially responsible investors. The increasing trend of corporate deceptions has made investors or fund managers consider the ethical assessments in their investment management. Therefore, it is essential to develop models capable of capturing the ethical and financial criteria in investment processes. In this study, a multi-stage methodology was proposed and linguistic Z-numbers were applied to represent the evaluation information. In addition, Muirhead Mean (MM) aggregation operators were employed to fuse the input data into the linguistic Z-number environment. To accomplish the objectives of this study, first, four linguistic Z-number MM operators were developed. Then, through the max-score rule and score-accuracy trade-off rule, three qualitative portfolio models were proposed. These models were established to maximize the financial performance of portfolio as their main objective, and they were distinguished by the ethical goal the investor follows. The obtained results of numerical example validated the capability of the models in constructing more diversified portfolio based on a trade-off between financial and ethical criteria according to the investors' preferences. (C) 2022 Sharif University of Technology. All rights reserved.