Linguistic Z-number weighted averaging operators and their application to portfolio selection problem

Abstract

Z-numbers can generate a more flexible structure to model the real information because of capturing expert's reliability. Moreover, various semantics can flexibly be reflected by linguistic terms under various circumstances. Thus, this study aims to model the portfolio selection problems based on aggregation operators under linguistic Z-number environment. Therefore, a multi-stage methodology is proposed and linguistic Z-numbers are applied to describe the assessment information. Moreover, the weighted averaging (WA) aggregation operator, the ordered weighted averaging (OWA) aggregation operator and the hybrid weighted averaging (HWA) aggregation operator are developed to fuse the input arguments under the linguistic Z-number environment. Then, using the max-score rule and the scoreaccuracy trade-off rule, three qualitative portfolio models are presented to allocate the optimal assets. These models are suitable for general investors and risky investors. Finally, to illustrate the validity of the proposed qualitative approach, a real case including 20 corporations of Tehran stock exchange market in Iran is provided and the obtained results are analyzed. The results show that combining linguistic Z-numbers with portfolio selection processes can increase the tendencies and capabilities of investors in the capital market and it helps them manage their portfolios efficiently.

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

“…From Table 9, it can be found that the assets selected by LZBM and LZGBM operators are slightly different from the assets obtained by LZWA, LZOWA and LZHWA operators [40]. This difference displays an advantage of the proposed aggregation operators which capture the interrelationship between input arguments, while Mahmoodi et al methods [40] suppose the input arguments are independent.…”

“…In order to further investigate the validity of the proposed aggregation operators, we compare them with Mahmoodi et al methods [40] built on some linguistic Z-number weighted averaging operators. The selected assets obtained by Model 2 are shown in Table 9.…”

“…Peng and Wang [38] developed the hesitant uncertain linguistic Z-number power weighted average operator and the hesitant uncertain linguistic Z-number power weighted geometric operator. Also, Mahmoodi et al [40] proposed three weighted averaging (WA) aggregation operators, which is called linguistic Z-number weighted averaging (LZWA), linguistic Z-number ordered weighted averaging (LZOWA) and linguistic Z-number hybrid weighted averaging (LZHWA). The main deficiency of these aggregation operators is that they do not consider the interrelationship of input data and suppose that all input arguments are independent.…”

A novel two-phase robust portfolio selection and optimization approach under uncertainty: A case study of Tehran stock exchange

“…The central of this interval at the point α ab is a nominal value andâ ab is the perturbation of uncertain parameters α ab ,b 2 Λ a . Finally, robust counterpart of constraint a based on Soyster [108], Ben-Tal & Nemirovski [109] and Bertsimas & Sim [110] robust optimization approaches are proposed as Eqs (10) to (12), respectively:…”

“…Another point that should be considered in the proposed approach for portfolio construction is the uncertain nature of parameters [9][10][11][12]. Because in the real-world, we face uncertain data, and one of the most important features of financial markets is their embedded uncertainty.…”