**6. Conclusions**

The main contribution of this paper is that a novel MAGDM model is proposed. In the proposed model, *q*-RPLNs are utilized to represent decision-makers' assessments of alternatives and weights of attributes and decision-makers take the form of crisp numbers. In addition, *q*-RPLHM, *q*-RPLWHM, *q*-RPLGHM, and *q*-RPLWGHM operators are proposed to aggregate attribute values to obtain overall assessments of alternatives. In order to do this, we proposed the *q*-RPFS and *q*-RPLS, which are powerful and effective tools for coping with uncertainty and vagueness. Subsequently, the operations and comparison law for *q*-RPLNs were introduced. We also proposed some aggregation operators for fusing *q*-rung picture linguistic information. The prominent characteristic of these operators is that they can capture the interrelationship between *q*-RPLNs. Moreover, we have studied some desirable properties and special cases of the proposed operators. Thereafter, we utilized the proposed operators to establish a novel method to solve MAGDM problems. To illustrate the validity of the proposed method, we used the proposed method to solve an ERP system selection problem. In addition, we conducted comparative analysis to demonstrate the effectiveness and superiorities of the proposed method. Due to the high ability of *q*-RPLSs for describing fuzziness and expressing decision-makers' assessments over alternatives, and the powerfulness of *q*-rung picture linguistic Heronian mean operators, the proposed method can be applied to solving real decision-making problems, such as supplier selection, low carbon supplier selection, hospital-based post-acute care, risk management, medical diagnosis, and resource evaluation, etc. In future works, considering the advantages of *q*-RPLSs, we should investigate more aggregation operators for fusing *q*-rung picture linguistic information such as the *q*-rung picture linguistic Bonferroni mean, *q*-rung picture linguistic Maclaurin symmetric mean, *q*-rung picture linguistic Hamy mean, and *q*-rung picture linguistic Muirhead mean. Additionally, we should investigate more methods of MAGDM with *q*-rung picture linguistic information.

**Author Contributions:** The idea of the whole thesis was put forward by L.L. She also wrote the paper. R.Z. analyzed the existing work and J.W. provided the numerical instance. The computation of the paper was conducted by X.S. and K.B.

**Acknowledgments:** This work was partially supported by National Natural Science Foundation of China (Grant number 71532002, 61702023), and the Fundamental Fund for Humanities and Social Sciences of Beijing Jiaotong University (Grant number 2016JBZD01).

**Conflicts of Interest:** The authors declare no conflict of interest.
