A visibility graph power averaging aggregation operator: A methodology based on network analysis

- A novel aggregation operator is proposed based on network analysis.
- It combines the advantages of the P- A operator and VGA operator.
- A new support function is proposed which is more objective and reasonable.
- Time factors are taken into consideration to show the rationality.
- An application in the analysis of the TAIEX is presented to show its validity.

Aggregation operators are widely used in many fields. Motivated by the idea of the visibility graph averaging (VGA) operator, in this paper, a visibility graph power averaging (VGPA) aggregation operator is proposed based on network analysis, since the visibility graph can convert a time series into a graph and save time information effectively. In our method, a new support function based on distance is proposed to measure the support degree of each other. The advantage is that the VGPA operator fully takes into account not only the relationship but also the correlation degree between the values. Compared with VGA operator, numerical results show more effectiveness on the proposed operator. Finally, the analysis of the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) is used to illustrate the application of the VGPA operator. In addition, the aggregated results compared with other operators show that our proposed method is more reasonable and effective in time series.