Abstract
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.
Highlights
Decision-making is an inseparable fact in the real world and people always encounter different decisions in daily life
We propose a qualitative approach to model cardinality constrained portfolio selection problem based on linguistic Z-number Bonferroni mean (LZBM) and linguistic Z-number geometric Bonferroni mean (LZGBM) operators under linguistic Z-number environment, and we use the max-score rule and the score-accuracy trade-off rule to formulate the models
The main steps of the extended methodology are: (i) extending two aggregation operators under linguistic Z-number environment and introducing LZBM operator and LZGBM operator to combine the linguistic Z-number information; (ii) proposing two qualitative hybrid portfolio optimization models under linguistic Z-number environment to assist investors for more flexible and more credible selecting the optimal portfolios according to their preferences
Summary
Decision-making is an inseparable fact in the real world and people always encounter different decisions in daily life. BM and GBM operators aggregate assessment information under linguistic Z-number environment and the aggregated values are applied to formulate portfolio selection problem based on the max-score rule and the scoreaccuracy trade-off rule. Since linguistic Z-numbers are more general structures to represent the real world information and incorporate possibilistic and probabilistic constraint, we apply the concept of linguistic Z-numbers to better describe and evaluate the future performance of each asset with respect to different criteria. 3. We propose a qualitative approach to model cardinality constrained portfolio selection problem based on LZBM and LZGBM operators under linguistic Z-number environment, and we use the max-score rule and the score-accuracy trade-off rule to formulate the models.
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