# A VIKOR-Based Sequential Three-Way Classification Ranking Method
## 2 Preliminaries
### Sequential Three-Way VIKOR Model Based on Minimum Group Utility Value
This indicates that the method proposed in this study is comparable to the other methods to some extent. In summary, the proposed method demonstrates a certain level of superiority and effectiveness. ## 6 Conclusions

This paper proposes a three-way sequential classification ranking method based on the VIKOR method. Firstly, based on the single regret value and group utility value, two different sequential three-way VIKOR models based on single regret value or group utility value are proposed. One shortcoming of the two models is that referring to partial decision information may bring errors in classification and ranking. This paper proposed a three-way sequential VIKOR model according to individual regret value and group utility value to compensate for the errors in classification and ranking. Secondly, the VIKOR method is introduced into three-way sequential decisions to design a three-way VIKOR method that can deal with both ranking and classification. This can effectively solve the problem of classification ranking and divide alternatives that are difficult to judge into the boundary region, reducing the possibility of misclassification leading to differences in ranking results. This study extends the application scope of the VIKOR method and sequential three-way decisions. Based on the experimental results, the effectiveness and feasibility of the method are confirmed. In the decision-making process, the advantages of the two methods are combined. By comprehensively considering the ranking index of the VIKOR method and \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Different Methods** & **Ours** & **[PERSON] [6]** & **[PERSON] [29]** & **[PERSON] [30]** & **[PERSON] [31]** & **VIKOR [28]** & **TOPSIS [32]** \\ \hline ours & 1 & 0.952 & 0.922 & 0.994 & 0.976 & 1 & 0.976 \\ [PERSON]’s method [6] & - & 1 & 0.898 & 0.970 & 0.976 & 0.952 & 0.976 \\ [PERSON]’s method [29] & - & - & 1 & 0.916 & 0.922 & 0.922 & 0.922 \\ [PERSON]’s method [30] & - & - & - & 1 & 0.970 & 0.994 & 0.970 \\ [PERSON]’s method [31] & - & - & - & - & 1 & 0.976 & 1 \\ VIKOR method [28] & - & - & - & - & - & 1 & 0.976 \\ TOPSIS method [32] & - & - & - & - & - & - & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Spearman correlation coefficient between the proposed method and other methods. Figure 8: Heatmap of Spearman correlation coefficient. the hierarchy and the division of decision domains for sequential three-way decisions, the possibility of misclassification and discrepancies in ranking results is reduced, leading to more scientific decision making. Next, the related models were improved and supplemented in terms of weight allocation, multi-criteria preference, extension, and improvement of the VIKOR method. The VIKOR method based on sequential three-way decisions in more complex decision problems is further explored and applied to solve sequencing and investment decision problems. In addition, the effective integration of other multi-attribute decision-making methods and three-way decisions will continue to be explored. Conceptualization, W.X. and J.Q. ; methodology, W.X. ; software, S.Y. ; validation, W.X. ; formal analysis, Y.W. ; investigation, Y.N. ; resources, J.Q. ; data curation, G.Y. ; writing--original draft preparation, W.X. ; writing--review and editing, W.X. ; visualization, W.X. ; supervision, J.Q. ; project administration, J.Q. ; funding acquisition, J.Q. All authors have read and agreed to the published version of the manuscript. This research was funded by [National Natural Science Foundation of China] grant number [62466017, 62066014, 62163016] and [Double thousand plan of Jiangxi Province of China, the Natural Science Foundation of Jiangxi Province] grant number [20232 ACB202013]. And The APC was funded by [National Natural Science Foundation of China]. All data generated or analyzed during this study are include in this published article. The authors declare no conflict of interest.