Table 8 The standardized inner-layer decision matrix.

From: A multi-dimensional decision framework based on the XGBoost algorithm and the constrained parametric approach

 

\({s}_{-2}\)

\({s}_{-1}\)

\({s}_{0}\)

\({s}_{1}\)

\({s}_{2}\)

\({A}_{1}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4892\right)\\ {n}_{0}\left(0.3869\right)\\ {n}_{1}\left(0.1238\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4786\right)\\ {n}_{0}\left(0.4345\right)\\ {n}_{1}\left(0.0870\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4678\right)\\ {n}_{0}\left(0.4393\right)\\ {n}_{1}\left(0.0929\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4333\right)\\ {n}_{0}\left(0.4679\right)\\ {n}_{1}\left(0.0988\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4274\right)\\ {n}_{0}\left(0.4702\right)\\ {n}_{1}\left(0.1024\right)\end{array}\right\}\)

\({A}_{2}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4953\right)\\ {n}_{0}\left(0.3964\right)\\ {n}_{1}\left(0.1083\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.3929\right)\\ {n}_{0}\left(0.5048\right)\\ {n}_{1}\left(0.1024\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4357\right)\\ {n}_{0}\left(0.4702\right)\\ {n}_{1}\left(0.0941\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4857\right)\\ {n}_{0}\left(0.4107\right)\\ {n}_{1}\left(0.1036\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.5143\right)\\ {n}_{0}\left(0.3845\right)\\ {n}_{1}\left(0.1012\right)\end{array}\right\}\)

\({A}_{3}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4083\right)\\ {n}_{0}\left(0.4797\right)\\ {n}_{1}\left(0.1119\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4690\right)\\ {n}_{0}\left(0.4084\right)\\ {n}_{1}\left(0.1226\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.3964\right)\\ {n}_{0}\left(0.4870\right)\\ {n}_{1}\left(0.1167\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4000\right)\\ {n}_{0}\left(0.4988\right)\\ {n}_{1}\left(0.1012\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4762\right)\\ {n}_{0}\left(0.4191\right)\\ {n}_{1}\left(0.1048\right)\end{array}\right\}\)

\({A}_{4}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4488\right)\\ {n}_{0}\left(0.4202\right)\\ {n}_{1}\left(0.1310\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4929\right)\\ {n}_{0}\left(0.4369\right)\\ {n}_{1}\left(0.0702\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4440\right)\\ {n}_{0}\left(0.4405\right)\\ {n}_{1}\left(0.1155\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4036\right)\\ {n}_{0}\left(0.4691\right)\\ {n}_{1}\left(0.1274\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4250\right)\\ {n}_{0}\left(0.4666\right)\\ {n}_{1}\left(0.1084\right)\end{array}\right\}\)

\({A}_{5}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4429\right)\\ {n}_{0}\left(0.4964\right)\\ {n}_{1}\left(0.0607\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4703\right)\\ {n}_{0}\left(0.3988\right)\\ {n}_{1}\left(0.1310\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4988\right)\\ {n}_{0}\left(0.4144\right)\\ {n}_{1}\left(0.0869\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4821\right)\\ {n}_{0}\left(0.3822\right)\\ {n}_{1}\left(0.1357\right)\end{array}\right\}\)

\(\left\{\begin{array}{c}{n}_{-1}\left(0.4785\right)\\ {n}_{0}\left(0.3929\right)\\ {n}_{1}\left(0.1286\right)\end{array}\right\}\)

  1. Sources: Authors’ own research.