Linguistic Z-Number Bonferroni Mean and Linguistic Z-Number Geometric Bonferroni Mean Operators: Their Applications in Portfolio Selection Problems

The optimal combination of assets can be selected by the traditional portfolio theory which uses historical quantitative data to represent the future return of assets. However, quantitative information is inaccessible in most cases and experts can help investors and fund managers by providing qualitative information. According to above discussion, a new multi-stage qualitative approach is proposed to select the optimal portfolio under linguistic Z-number environment. To achieve this aim, this study firstly develops the Bonferroni mean (BM) operator and the geometric Bonferroni mean (GBM) operator under the linguistic Z-number environment, and introduces linguistic Z-number Bonferroni mean (LZBM) operator and linguistic Z-number geometric Bonferroni mean (LZGBM) operator to aggregate the qualitative evaluation information. Then, using the developed aggregation operators, two qualitative portfolio selection models are proposed based on the max-score rule and the score-accuracy trade-off rule for the general investors and risky investors, respectively. Finally, to illustrate the validity of the proposed models, a case study including 20 corporations of Tehran stock exchange market in Iran is provided and the obtained results are analyzed. Moreover, the qualitative proposed models are compared with another available model. The obtained results indicate that the qualitative proposed approach can help investors and fund managers to make more credible decisions so that they can select the optimal assets with considering different criteria when experts are assured about their assessments or opinions. Therefore, the qualitative proposed models are superior and more general in comparison with the other ones due to capturing the reliability of information. Also, the obtained results show the influence of reliability measures in investment processes.