Table 16 Weight-normalized decision \({DM}_{1}\), \({DM}_{2}\), \({DM}_{3}\) information \((DM{(N}_{ij}^{1}\))),\((DM{(N}_{ij}^{2}\))), and \((DM{(N}_{ij}^{3}\))).
\({\varvec{D}}{{\varvec{M}}}_{1}\) | \({{\varvec{C}}}_{1}\) | \({{\varvec{C}}}_{2}\) | \({{\varvec{C}}}_{3}\) | \({{\varvec{C}}}_{4}\) | \({{\varvec{C}}}_{5}\) |
---|---|---|---|---|---|
\({{\varvec{P}}}_{1}\) | \(\left(\begin{array}{c}0.450, 0.676\\ \mathrm{0.648,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.448, 0.677\\ \mathrm{0.646,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.021, 0.685\\ \mathrm{0.021,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.644, 0.679\\ \mathrm{0.021,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.634, 0.689\\ \mathrm{0.021,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{2}\) | \(\left(\begin{array}{c}0.080, 0.676\\ \mathrm{0.648,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.080, 0.677\\ \mathrm{0.048,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.639, 0.685\\ \mathrm{0.164,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.320, 0.679\\ \mathrm{0.644,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.634, 0.689\\ \mathrm{0.021,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{3}\) | \(\left(\begin{array}{c}0.048, 0.676\\ \mathrm{0.022,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.048, 0.677\\ \mathrm{0.646,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.077, 0.685\\ \mathrm{0.314,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.118, 0.679\\ \mathrm{0.048,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.046, 0.689\\ \mathrm{0.634,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{4}\) | \(\left(\begin{array}{c}0.323, 0.676\\ \mathrm{0.234,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.448, 0.677\\ \mathrm{0.080,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.164, 0.685\\ 0.44\mathrm{0,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.118, 0.679\\ \mathrm{0.118,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.435, 0.689\\ \mathrm{0.634,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{5}\) | \(\left(\begin{array}{c}0.234, 0.676\\ \mathrm{0.323,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.022, 0.677\\ \mathrm{0.080,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.228, 0.685\\ \mathrm{0.021,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.446, 0.679\\ \mathrm{0.320,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.634, 0.689\\ \mathrm{0.021,0.689}\end{array}\right)\) |
\({\varvec{D}}{{\varvec{M}}}_{2}\) | \({C}_{1}\) | \({C}_{2}\) | \({C}_{3}\) | \({C}_{4}\) | \({C}_{5}\) |
\({{\varvec{P}}}_{1}\) | \(\left(\begin{array}{c}0.323, 0.676\\ 0.323, 0.676\end{array}\right)\) | \(\left(\begin{array}{c}0.646, 0.677\\ 0.022, 0.677\end{array}\right)\) | \(\left(\begin{array}{c}0.639, 0.685\\ \mathrm{0.648,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.644, 0.679\\ \mathrm{0.021,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.435, 0.689\\ \mathrm{0.634,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{2}\) | \(\left(\begin{array}{c}0.169, 0.676\\ \mathrm{0.234,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.048, 0.677\\ \mathrm{0.646,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.077, 0.685\\ \mathrm{0.021,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.048, 0.679\\ \mathrm{0.644,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.114, 0.689\\ \mathrm{0.634,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{3}\) | \(\left(\begin{array}{c}0.048, 0.676\\ \mathrm{0.648,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.169, 0.677\\ \mathrm{0.080,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.164, 0.685\\ \mathrm{0.046,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.079, 0.679\\ \mathrm{0.079,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.161, 0.689\\ \mathrm{0.224,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{4}\) | \(\left(\begin{array}{c}0.022, 0.676\\ \mathrm{0.169,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.448, 0.677\\ \mathrm{0.646,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.639, 0.685\\ \mathrm{0.440,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.664, 0.679\\ \mathrm{0.664,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.310, 0.689\\ \mathrm{0.435,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{5}\) | \(\left(\begin{array}{c}0.080, 0.676\\ \mathrm{0.234,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.646, 0.677\\ \mathrm{0.022,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.639, 0.685\\ \mathrm{0.440,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.232, 0.679\\ \mathrm{0.644,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.046, 0.689\\ \mathrm{0.634,0.689}\end{array}\right)\) |
\({\varvec{D}}{{\varvec{M}}}_{3}\) | \({C}_{1}\) | \({C}_{2}\) | \({C}_{3}\) | \({C}_{4}\) | \({C}_{5}\) |
\({{\varvec{P}}}_{1}\) | \(\left(\begin{array}{c}0.048, 0.676\\ \mathrm{0.450,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.080, 0.677\\ \mathrm{0.448,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.046, 0.685\\ \mathrm{0.164,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.446, 0.679\\ \mathrm{0.446,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.310, 0.689\\ \mathrm{0.634,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{2}\) | \(\left(\begin{array}{c}0.323, 0.676\\ \mathrm{0.450,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.119, 0.677\\ \mathrm{0.646,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.021, 0.685\\ \mathrm{0.164,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.664, 0.679\\ \mathrm{0.644,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.046, 0.689\\ \mathrm{0.021,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{3}\) | \(\left(\begin{array}{c}0.080, 0.676\\ \mathrm{0.234,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.233, 0.677\\ \mathrm{0.119,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.077, 0.685\\ \mathrm{0.228,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.118, 0.679\\ \mathrm{0.644,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.435, 0.689\\ \mathrm{0.076,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{4}\) | \(\left(\begin{array}{c}0.048, 0.676\\ \mathrm{0.648,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.322, 0.677\\ \mathrm{0.448,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.440, 0.685\\ \mathrm{0.639,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.644, 0.679\\ \mathrm{0.118,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.310, 0.689\\ \mathrm{0.224,0.689}\end{array}\right)\) |
\({{\varvec{P}}}_{5}\) | \(\left(\begin{array}{c}0.169, 0.676\\ \mathrm{0.120,0.676}\end{array}\right)\) | \(\left(\begin{array}{c}0.048, 0.677\\ \mathrm{0.646,0.677}\end{array}\right)\) | \(\left(\begin{array}{c}0.440, 0.685\\ \mathrm{0.639,0.685}\end{array}\right)\) | \(\left(\begin{array}{c}0.644, 0.679\\ \mathrm{0.118,0.679}\end{array}\right)\) | \(\left(\begin{array}{c}0.224, 0.689\\ \mathrm{0.310,0.689}\end{array}\right)\) |