Introduction
Preliminaries
Novel decision model with PHFEs
Imputation of non-available entries
Mathematical model for expert weight estimation
Mathematical model for criteria weight determination
PHFS-based Hamy mean operator
New extension to COPRAS method
Numerical example
Criteria | DMs | Cloud vendors | |||||
---|---|---|---|---|---|---|---|
\({A}_{1}\) | \({A}_{2}\) | \({A}_{3}\) | \({A}_{4}\) | \({A}_{5}\) | \({A}_{6}\) | ||
\({B}_{1}\) | \({D}_{1}\) | \(\left( \begin{gathered} \left( {0.66, \, 0.66} \right), \hfill \\ \left( {0.69, \, 0.24} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.11, \, 0.33} \right), \hfill \\ \left( {0.63, \, 0.29} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.54, \, 0.64} \right), \hfill \\ \,\left( {0.59, \, 0.1} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.32, \, 0.25} \right), \hfill \\ \left( {0.14, \, 0.42} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.67, \, 0.42} \right), \hfill \\ \left( {0.62, \, 0.51} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.34, \, 0.17} \right), \hfill \\ \left( {0.41, \, 0.43} \right) \hfill \\ \end{gathered} \right)\) |
\({D}_{2}\) | \(\left( \begin{gathered} \left( {0.15, \, 0.15} \right), \hfill \\ \left( {0.35, \, 0.34} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.44, \, 0.49} \right), \hfill \\ \left( {0.43, \, 0.25} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.41, \, 0.48} \right), \hfill \\ \left( {0.57, \, 0.44} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.76, \, 0.27} \right), \hfill \\ \left( {0.69, \, 0.57} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.72, \, 0.6} \right), \hfill \\ \left( {0.61, \, 0.39} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.43, \, 0.17} \right), \hfill \\ \left( {0.54, \, 0.46} \right) \hfill \\ \end{gathered} \right)\) | |
\({D}_{3}\) | \(\left( \begin{gathered} \left( {0.19, \, 0.11} \right), \hfill \\ \left( {0.33, \, 0.17} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.33, \, 0.29} \right), \hfill \\ \left( {0.48, \, 0.25} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.6, \, 0.14} \right), \hfill \\ \left( {0.58, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.45, \, 0.15} \right), \hfill \\ \left( {0.69, \, 0.44} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.2, \, 0.11} \right), \hfill \\ \left( {0.78, \, 0.19} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.63, \, 0.19} \right), \hfill \\ \left( {0.19, \, 0.71} \right) \hfill \\ \end{gathered} \right)\) | |
\({B}_{2}\) | \({D}_{1}\) | \(\left( \begin{gathered} \left( {0.44, \, 0.57} \right), \hfill \\ \left( {0.75, \, 0.21} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.54, \, 0.18} \right), \hfill \\ \left( {0.28, \, 0.62} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.17, \, 0.35} \right), \hfill \\ \left( {0.54, \, 0.59} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.25, \, 0.33} \right), \hfill \\ \left( {0.47, \, 0.54} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.63, \, 0.14} \right), \hfill \\ \left( {0.38, \, 0.13} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.59, \, 0.37} \right), \hfill \\ \left( {0.27, \, 0.15} \right) \hfill \\ \end{gathered} \right)\) |
\({D}_{2}\) | \(\left( \begin{gathered} \left( {0.52, \, 0.22} \right), \hfill \\ \left( {0.50, \, 0.61} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.16, \, 0.54} \right), \hfill \\ \left( {0.76, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.38, \, 0.39} \right), \hfill \\ \left( {0.13, \, 0.13} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.76, \, 0.13} \right), \hfill \\ \left( {0.54, \, 0.46} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.60, \, 0.31} \right), \hfill \\ \left( {0.72, \, 0.60} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.51, \, 0.59} \right), \hfill \\ \left( {0.70, \, 0.12} \right) \hfill \\ \end{gathered} \right)\) | |
\({D}_{3}\) | \(\left( \begin{gathered} \left( {0.58, \, 0.61} \right), \hfill \\ \left( {0.37, \, 0.21} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.29, \, 0.22} \right), \hfill \\ \left( {0.31, \, 0.68} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.54, \, 0.13} \right), \hfill \\ \left( {0.34, \, 0.31} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.25, \, 0.25} \right), \hfill \\ \left( {0.32, \, 0.73} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.78, \, 0.26} \right), \hfill \\ \left( {0.16, \, 0.69} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.80, \, 0.51} \right), \hfill \\ \left( {0.16, \, 0.28} \right) \hfill \\ \end{gathered} \right)\) | |
\({B}_{3}\) | \({D}_{1}\) | \(\left( \begin{gathered} \left( {0.39, \, 0.31} \right), \hfill \\ \left( {0.30, \, 0.23} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.26, \, 0.14} \right), \hfill \\ \left( {0.43, \, 0.44} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.45, \, 0.63} \right), \hfill \\ \left( {0.59, \, 0.27} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.52, \, 0.62} \right), \hfill \\ \left( {0.40, \, 0.31} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.26, \, 0.20} \right), \hfill \\ \left( {0.65, \, 0.68} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.80, \, 0.36} \right), \hfill \\ \left( {0.13, \, 0.16} \right) \hfill \\ \end{gathered} \right)\) |
\({D}_{2}\) | \(\left( \begin{gathered} \left( {0.71, \, 0.60} \right), \hfill \\ \left( {0.71, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.57, \, 0.29} \right), \hfill \\ \left( {0.19, \, 0.40} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.44, \, 0.21} \right), \hfill \\ \left( {0.10, \, 0.21} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.30, \, 0.21} \right), \hfill \\ \left( {0.69, \, 0.43} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.21, \, 0.72} \right), \hfill \\ \left( {0.58, \, 0.23} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.31, \, 0.15} \right), \hfill \\ \left( {0.12, \, 0.19} \right) \hfill \\ \end{gathered} \right)\) | |
\({D}_{3}\) | \(\left( \begin{gathered} \left( {0.72, \, 0.12} \right), \hfill \\ \left( {0.49, \, 0.55} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.61, \, 0.63} \right), \hfill \\ \left( {0.74, \, 0.36} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.56, \, 0.33} \right), \hfill \\ \left( {0.21, \, 0.42} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.48, \, 0.18} \right), \hfill \\ \left( {0.30, \, 0.68} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.11, \, 0.44} \right), \hfill \\ \left( {0.43, \, 0.14} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.49, \, 0.43} \right), \hfill \\ \left( {0.75, \, 0.11} \right) \hfill \\ \end{gathered} \right)\) | |
\({B}_{4}\) | \({D}_{1}\) | \(\left( \begin{gathered} \left( {0.49, \, 0.28} \right), \hfill \\ \left( {0.49, \, 0.38} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.67, \, 0.31} \right), \hfill \\ \left( {0.34, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.57, \, 0.65} \right), \hfill \\ \left( {0.72, \, 0.24} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.29, \, 0.28} \right), \hfill \\ \left( {0.15, \, 0.56} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.66, \, 0.65} \right), \hfill \\ \left( {0.29, \, 0.27} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.42, \, 0.67} \right), \hfill \\ \left( {0.57, \, 0.24} \right) \hfill \\ \end{gathered} \right)\) |
\({D}_{2}\) | \(\left( \begin{gathered} \left( {0.79, \, 0.68} \right), \hfill \\ \left( {0.69, \, 0.12} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.58, \, 0.48} \right), \hfill \\ \left( {0.64, \, 0.11} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.37, \, 0.11} \right), \hfill \\ \left( {0.31, \, 0.67} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.12, \, 0.70} \right), \hfill \\ \left( {0.77, \, 0.20} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.28, \, 0.67} \right), \hfill \\ \left( {0.22, \, 0.22} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.26, \, 0.40} \right), \hfill \\ \left( {0.28, \, 0.45} \right) \hfill \\ \end{gathered} \right)\) | |
\({D}_{3}\) | \(\left( \begin{gathered} \left( {0.72, \, 0.20} \right), \hfill \\ \left( {0.76, \, 0.65} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.64, \, 0.17} \right), \hfill \\ \left( {0.26, \, 0.15} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.71, \, 0.13} \right), \hfill \\ \left( {0.72, \, 0.25} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.12, \, 0.77} \right), \hfill \\ \left( {0.19, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.43, \, 0.51} \right), \hfill \\ \left( {0.35, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.10, \, 0.10} \right), \hfill \\ \left( {0.62, \, 0.47} \right) \hfill \\ \end{gathered} \right)\) | |
\({B}_{5}\) | \({D}_{1}\) | \(\left( \begin{gathered} \left( {0.60, \, 0.31} \right), \hfill \\ \left( {0.43, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.60, \, 0.31} \right), \hfill \\ \left( {0.43, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.60, \, 0.31} \right), \hfill \\ \left( {0.43, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.37, \, 0.60} \right), \hfill \\ \left( {0.49, \, 0.28} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.73, \, 0.13} \right), \hfill \\ \left( {0.35, \, 0.62} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.62, \, 0.37} \right), \hfill \\ \left( {0.44, \, 0.20} \right) \hfill \\ \end{gathered} \right)\) |
\({D}_{2}\) | \(\left( \begin{gathered} \left( {0.66, \, 0.16} \right), \hfill \\ \left( {0.58, \, 0.14} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.35, \, 0.38} \right), \hfill \\ \left( {0.16, \, 0.57} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.23, \, 0.42} \right), \hfill \\ \left( {0.20, \, 0.38} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.61, \, 0.24} \right), \hfill \\ \left( {0.40, \, 0.68} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.75, \, 0.26} \right), \hfill \\ \left( {0.36, \, 0.17} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.62, \, 0.27} \right), \hfill \\ \left( {0.25, \, 0.50} \right) \hfill \\ \end{gathered} \right)\) | |
\({D}_{3}\) | \(\left( \begin{gathered} \left( {0.46, \, 0.12} \right), \hfill \\ \left( {0.53, \, 0.32} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.64, \, 0.17} \right), \hfill \\ \left( {0.20, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.53, \, 0.33} \right), \hfill \\ \left( {0.29, \, 0.19} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.76, \, 0.50} \right), \hfill \\ \left( {0.77, \, 0.13} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.46, \, 0.80} \right), \hfill \\ \left( {0.19, \, 0.15} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.21, \, 0.36} \right), \hfill \\ \left( {0.49, \, 0.27} \right) \hfill \\ \end{gathered} \right)\) | |
\({B}_{6}\) | \({D}_{1}\) | \(\left( \begin{gathered} \left( {0.63, \, 0.25} \right), \hfill \\ \left( {0.39, \, 0.42} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.11, \, 0.18} \right), \hfill \\ \left( {0.47, \, 0.22} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.15, \, 0.30} \right), \hfill \\ \left( {0.37, \, 0.48} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.50, \, 0.26} \right), \hfill \\ \left( {0.36, \, 0.68} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.74, \, 0.36} \right), \hfill \\ \left( {0.54, \, 0.38} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.63, \, 0.23} \right), \hfill \\ \left( {0.79, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) |
\({D}_{2}\) | \(\left( \begin{gathered} \left( {0.44, \, 0.42} \right), \hfill \\ \left( {0.34, \, 0.23} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.12, \, 0.15} \right), \hfill \\ \left( {0.48, \, 0.16} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.53, \, 0.38} \right), \hfill \\ \left( {0.37, \, 0.29} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.63, \, 0.28} \right), \hfill \\ \left( {0.31, \, 0.47} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.61, \, 0.43} \right), \hfill \\ \left( {0.39, \, 0.26} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.72, \, 0.11} \right), \hfill \\ \left( {0.23, \, 0.16} \right) \hfill \\ \end{gathered} \right)\) | |
\({D}_{3}\) | \(\left( \begin{gathered} \left( {0.15, \, 0.69} \right), \hfill \\ \left( {0.29, \, 0.13} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.12, \, 0.13} \right), \hfill \\ \left( {0.48, \, 0.11} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.74, \, 0.47} \right), \hfill \\ \left( {0.36, \, 0.17} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.73, \, 0.30} \right), \hfill \\ \left( {0.26, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.41, \, 0.51} \right), \hfill \\ \left( {0.20, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.53, \, 0.37} \right), \hfill \\ \left( {0.54, \, 0.40} \right) \hfill \\ \end{gathered} \right)\) | |
\({B}_{7}\) | \({D}_{1}\) | \(\left( \begin{gathered} \left( {0.77, \, 0.26} \right), \hfill \\ \left( {0.29, \, 0.57} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.71, \, 0.11} \right), \hfill \\ \left( {0.51, \, 0.27} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.49, \, 0.29} \right), \hfill \\ \left( {0.74, \, 0.20} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.19, \, 0.30} \right), \hfill \\ \left( {0.13, \, 0.19} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.23, \, 0.13} \right), \hfill \\ \left( {0.76, \, 0.52} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.75, \, 0.51} \right), \hfill \\ \left( {0.39, \, 0.13} \right) \hfill \\ \end{gathered} \right)\) |
\({D}_{2}\) | \(\left( \begin{gathered} \left( {0.29, \, 0.56} \right), \hfill \\ \left( {0.36, \, 0.30} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.79, \, 0.61} \right), \hfill \\ \left( {0.15, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.54, \, 0.53} \right), \hfill \\ \left( {0.30, \, 0.41} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.56, \, 0.26} \right), \hfill \\ \left( {0.40, \, 0.48} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.12, \, 0.18} \right), \hfill \\ \left( {0.73, \, 0.26} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.24, \, 0.53} \right), \hfill \\ \left( {0.79, \, 0.38} \right) \hfill \\ \end{gathered} \right)\) | |
\({D}_{3}\) | \(\left( \begin{gathered} \left( {0.17, \, 0.47} \right), \hfill \\ \left( {0.15, \, 0.40} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.15, \, 0.27} \right), \hfill \\ \left( {0.28, \, 0.16} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.29, \, 0.33} \right), \hfill \\ \left( {0.72, \, 0.13} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.48, \, 0.34} \right), \hfill \\ \left( {0.20, \, 0.52} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.32, \, 0.19} \right), \hfill \\ \left( {0.50, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.43, \, 0.40} \right), \hfill \\ \left( {0.55, \, 0.38} \right) \hfill \\ \end{gathered} \right)\) |
Criteria | DMs | ||
---|---|---|---|
\({D}_{1}\) | \({D}_{2}\) | \({D}_{3}\) | |
\({B}_{1}\) | \(\left( \begin{gathered} \left( {0.16, \, 0.42} \right), \hfill \\ \left( {0.22, \, 0.25} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.54, \, 0.18} \right), \hfill \\ \left( {0.75, \, 0.10} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.22, \, 0.65} \right), \hfill \\ \left( {0.54, \, 0.12} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{2}\) | \(\left( \begin{gathered} \left( {0.66, \, 0.22} \right), \hfill \\ \left( {0.37, \, 0.37} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.43, \, 0.51} \right), \hfill \\ \left( {0.16, \, 0.24} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.45, \, 0.50} \right), \hfill \\ \left( {0.49, \, 0.43} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{3}\) | \(\left( \begin{gathered} \left( {0.29, \, 0.36} \right), \hfill \\ \left( {0.14, \, 0.32} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.60, \, 0.39} \right), \hfill \\ \left( {0.24, \, 0.12} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.14, \, 0.25} \right), \hfill \\ \left( {0.79, \, 0.16} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{4}\) | \(\left( \begin{gathered} \left( {0.34, \, 0.35} \right), \hfill \\ \left( {0.64, \, 0.44} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.69, \, 0.31} \right), \hfill \\ \left( {0.28, \, 0.39} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.70, \, 0.32} \right), \hfill \\ \left( {0.10, \, 0.47} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{5}\) | \(\left( \begin{gathered} \left( {0.43, \, 0.25} \right), \hfill \\ \left( {0.39, \, 0.66} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.56, \, 0.32} \right), \hfill \\ \left( {0.40, \, 0.28} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.13, \, 0.27} \right), \hfill \\ \left( {0.55, \, 0.50} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{6}\) | \(\left( \begin{gathered} \left( {0.30, \, 0.24} \right), \hfill \\ \left( {0.48, \, 0.58} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.46, \, 0.27} \right), \hfill \\ \left( {0.39, \, 0.55} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.47, \, 0.55} \right), \hfill \\ \left( {0.56, \, 0.28} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{7}\) | \(\left( \begin{gathered} \left( {0.62, \, 0.21} \right), \hfill \\ \left( {0.57, \, 0.60} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.51, \, 0.40} \right), \hfill \\ \left( {0.50, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.11, \, 0.53} \right), \hfill \\ \left( {0.18, \, 0.44} \right) \hfill \\ \end{gathered} \right)\) |
Criteria | Ideal solutions | |
---|---|---|
\({h}_{j}^{+}\) | \({h}_{j}^{-}\) | |
\({B}_{1}\) | \(\left( \begin{gathered} \left( {0.22, \, 0.65} \right), \hfill \\ \left( {0.54, \, 0.12} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.16, \, 0.42} \right), \hfill \\ \left( {0.22, \, 0.25} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{2}\) | \(\left( \begin{gathered} \left( {0.45, \, 0.50} \right), \hfill \\ \left( {0.49, \, 0.43} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.43, \, 0.51} \right), \hfill \\ \left( {0.16, \, 0.24} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{3}\) | \(\left( \begin{gathered} \left( {0.60, \, 0.39} \right), \hfill \\ \left( {0.24, \, 0.12} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.29, \, 0.36} \right), \hfill \\ \left( {0.14, \, 0.32} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{4}\) | \(\left( \begin{gathered} \left( {0.34, \, 0.35} \right), \hfill \\ \left( {0.64, \, 0.44} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.7, \, 0.32} \right), \hfill \\ \left( {0.1, \, 0.47} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{5}\) | \(\left( \begin{gathered} \left( {0.43, \, 0.25} \right), \hfill \\ \left( {0.39, \, 0.66} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.56, \, 0.32} \right), \hfill \\ \left( {0.40, \, 0.28} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{6}\) | \(\left( \begin{gathered} \left( {0.46, \, 0.27} \right), \hfill \\ \left( {0.39, \, 0.55} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.47, \, 0.55} \right), \hfill \\ \left( {0.56, \, 0.28} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{7}\) | \(\left( \begin{gathered} \left( {0.11, \, 0.53} \right), \hfill \\ \left( {0.18, \, 0.44} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.62, \, 0.21} \right), \hfill \\ \left( {0.57, \, 0.60} \right) \hfill \\ \end{gathered} \right)\) |
Criteria | Ideal solutions | |
---|---|---|
\({h}_{j}^{+}\) | \({h}_{j}^{-}\) | |
\({{\varvec{B}}}_{1}\) | \(\left( \begin{gathered} \left( {0.66, \, 0.66} \right), \hfill \\ \left( {0.69, \, 0.24} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.32, \, 0.25} \right), \hfill \\ \left( {0.14, \, 0.42} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{2}\) | \(\left( \begin{gathered} \left( {0.44, \, 0.57} \right), \hfill \\ \left( {0.75, \, 0.21} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.63, \, 0.14} \right), \hfill \\ \left( {0.38, \, 0.13} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{3}\) | \(\left( \begin{gathered} \left( {0.26, \, 0.20} \right), \hfill \\ \left( {0.65, \, 0.68} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.39, \, 0.31} \right), \hfill \\ \left( {0.30, \, 0.23} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{4}\) | \(\left( \begin{gathered} \left( {0.57, \, 0.65} \right), \hfill \\ \left( {0.72, \, 0.24} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.29, \, 0.28} \right), \hfill \\ \left( {0.15, \, 0.56} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{5}\) | \(\left( \begin{gathered} \left( {0.37, \, 0.60} \right), \hfill \\ \left( {0.49, \, 0.28} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.73, \, 0.13} \right), \hfill \\ \left( {0.35, \, 0.62} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{6}\) | \(\left( \begin{gathered} \left( {0.11, \, 0.18} \right), \hfill \\ \left( {0.47, \, 0.22} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.74, \, 0.36} \right), \hfill \\ \left( {0.54, \, 0.38} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{7}\) | \(\left( \begin{gathered} \left( {0.19, \, 0.30} \right), \hfill \\ \left( {0.13, \, 0.19} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.75, \, 0.51} \right), \hfill \\ \left( {0.39, \, 0.13} \right) \hfill \\ \end{gathered} \right)\) |
\({{\varvec{B}}}_{1}\) | \(\left( \begin{gathered} \left( {0.72, \, 0.60} \right), \hfill \\ \left( {0.61, \, 0.39} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.15, \, 0.15} \right), \hfill \\ \left( {0.35, \, 0.34} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{2}\) | \(\left( \begin{gathered} \left( {0.60, \, 0.31} \right), \hfill \\ \left( {0.72, \, 0.60} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.38, \, 0.39} \right), \hfill \\ \left( {0.13, \, 0.13} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{3}\) | \(\left( \begin{gathered} \left( {0.71, \, 0.60} \right), \hfill \\ \left( {0.71, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.31, \, 0.15} \right), \hfill \\ \left( {0.12, \, 0.19} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{4}\) | \(\left( \begin{gathered} \left( {0.79, \, 0.68} \right), \hfill \\ \left( {0.69, \, 0.12} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.26, \, 0.40} \right), \hfill \\ \left( {0.28, \, 0.45} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{5}\) | \(\left( \begin{gathered} \left( {0.61, \, 0.24} \right), \hfill \\ \left( {0.40, \, 0.68} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.23, \, 0.42} \right), \hfill \\ \left( {0.20, \, 0.38} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{6}\) | \(\left( \begin{gathered} \left( {0.12, \, 0.15} \right), \hfill \\ \left( {0.48, \, 0.16} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.61, \, 0.43} \right), \hfill \\ \left( {0.39, \, 0.26} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{7}\) | \(\left( \begin{gathered} \left( {0.12, \, 0.18} \right), \hfill \\ \left( {0.73, \, 0.26} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.79, \, 0.61} \right), \hfill \\ \left( {0.15, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) |
\({{\varvec{B}}}_{1}\) | \(\left( \begin{gathered} \left( {0.45, \, 0.15} \right), \hfill \\ \left( {0.69, \, 0.44} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.19, \, 0.11} \right), \hfill \\ \left( {0.33, \, 0.17} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{2}\) | \(\left( \begin{gathered} \left( {0.80, \, 0.51} \right), \hfill \\ \left( {0.16, \, 0.28} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.54, \, 0.13} \right), \hfill \\ \left( {0.34, \, 0.31} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{3}\) | \(\left( \begin{gathered} \left( {0.61, \, 0.63} \right), \hfill \\ \left( {0.74, \, 0.36} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.11, \, 0.44} \right), \hfill \\ \left( {0.43, \, 0.14} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{4}\) | \(\left( \begin{gathered} \left( {0.72, \, 0.20} \right), \hfill \\ \left( {0.76, \, 0.65} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.12, \, 0.77} \right), \hfill \\ \left( {0.19, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{5}\) | \(\left( \begin{gathered} \left( {0.76, \, 0.50} \right), \hfill \\ \left( {0.77, \, 0.13} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.64, \, 0.17} \right), \hfill \\ \left( {0.20, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{6}\) | \(\left( \begin{gathered} \left( {0.12, \, 0.13} \right), \hfill \\ \left( {0.48, \, 0.11} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.53, \, 0.37} \right), \hfill \\ \left( {0.54, \, 0.40} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{7}\) | \(\left( \begin{gathered} \left( {0.15, \, 0.27} \right), \hfill \\ \left( {0.28, \, 0.16} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.43, \, 0.40} \right), \hfill \\ \left( {0.55, \, 0.38} \right) \hfill \\ \end{gathered} \right)\) |
Criteria | Cloud vendors | |||||
---|---|---|---|---|---|---|
\({A}_{1}\) | \({A}_{2}\) | \({A}_{3}\) | \({A}_{4}\) | \({A}_{5}\) | \({A}_{6}\) | |
\({B}_{1}\) | \(\left( \begin{gathered} \left( {0.50, \, 0.50} \right), \hfill \\ \left( {0.54, \, 0.29} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.37, \, 0.41} \right), \hfill \\ \left( {0.53, \, 0.26} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.53, \, 0.52} \right), \hfill \\ \left( {0.58, \, 0.37} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.64, \, 0.24} \right), \hfill \\ \left( {0.64, \, 0.50} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.65, \, 0.50} \right), \hfill \\ \left( {0.68, \, 0.42} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.51, \, 0.18} \right), \hfill \\ \left( {0.46, \, 0.58} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{2}\) | \(\left( \begin{gathered} \left( {0.52, \, 0.53} \right), \hfill \\ \left( {0.61, \, 0.49} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.41, \, 0.44} \right), \hfill \\ \left( {0.63, \, 0.58} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.43, \, 0.34} \right), \hfill \\ \left( {0.42, \, 0.45} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.62, \, 0.26} \right), \hfill \\ \left( {0.48, \, 0.61} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.68, \, 0.27} \right), \hfill \\ \left( {0.59, \, 0.59} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.67, \, 0.52} \right), \hfill \\ \left( {0.57, \, 0.21} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{3}\) | \(\left( \begin{gathered} \left( {0.67, \, 0.49} \right), \hfill \\ \left( {0.60, \, 0.41} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.54, \, 0.48} \right), \hfill \\ \left( {0.58, \, 0.40} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.49, \, 0.48} \right), \hfill \\ \left( {0.44, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.45, \, 0.47} \right), \hfill \\ \left( {0.57, \, 0.54} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.22, \, 0.60} \right), \hfill \\ \left( {0.58, \, 0.52} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.64, \, 0.35} \right), \hfill \\ \left( {0.57, \, 0.17} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{4}\) | \(\left( \begin{gathered} \left( {0.72, \, 0.55} \right), \hfill \\ \left( {0.68, \, 0.50} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.63, \, 0.40} \right), \hfill \\ \left( {0.52, \, 0.15} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.59, \, 0.49} \right), \hfill \\ \left( {0.65, \, 0.54} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.22, \, 0.68} \right), \hfill \\ \left( {0.63, \, 0.42} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.52, \, 0.63} \right), \hfill \\ \left( {0.30, \, 0.23} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.33, \, 0.52} \right), \hfill \\ \left( {0.53, \, 0.42} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{5}\) | \(\left( \begin{gathered} \left( {0.60, \, 0.24} \right), \hfill \\ \left( {0.53, \, 0.29} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.56, \, 0.33} \right), \hfill \\ \left( {0.32, \, 0.47} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.51, \, 0.37} \right), \hfill \\ \left( {0.34, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.34, \, 0.22} \right), \hfill \\ \left( {0.44, \, 0.55} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.70, \, 0.62} \right), \hfill \\ \left( {0.33, \, 0.47} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.57, \, 0.34} \right), \hfill \\ \left( {0.42, \, 0.41} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{6}\) | \(\left( \begin{gathered} \left( {0.50, \, 0.54} \right), \hfill \\ \left( {0.35, \, 0.32} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.12, \, 0.16} \right), \hfill \\ \left( {0.48, \, 0.18} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.60, \, 0.40} \right), \hfill \\ \left( {0.37, \, 0.37} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.64, \, 0.28} \right), \hfill \\ \left( {0.32, \, 0.55} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.63, \, 0.45} \right), \hfill \\ \left( {0.44, \, 0.30} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.65, \, 0.28} \right), \hfill \\ \left( {0.63, \, 0.30} \right) \hfill \\ \end{gathered} \right)\) |
\({B}_{7}\) | \(\left( \begin{gathered} \left( {0.59, \, 0.49} \right), \hfill \\ \left( {0.31, \, 0.46} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.71, \, 0.49} \right), \hfill \\ \left( {0.39, \, 0.22} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.48, \, 0.44} \right), \hfill \\ \left( {0.66, \, 0.33} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.49, \, 0.30} \right), \hfill \\ \left( {0.32, \, 0.46} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.25, \, 0.17} \right), \hfill \\ \left( {0.70, \, 0.41} \right) \hfill \\ \end{gathered} \right)\) | \(\left( \begin{gathered} \left( {0.59, \, 0.49} \right), \hfill \\ \left( {0.68, \, 0.35} \right) \hfill \\ \end{gathered} \right) \) |
Cloud vendors | COPRAS parameters | ||
---|---|---|---|
\({R1}_{i}^{k}\) | \({R2}_{i}^{k}\) | \({R3}_{i}\) | |
\({A}_{1}\) | (0.54, 0.55) (0.53, 0.49) | (0.15, 0.88) (0.08, 0.83) | 4.70 |
\({A}_{2}\) | (0.44, 0.50) (0.47, 0.41) | (0.13, 0.78) (0.11, 0.72) | 5.12 |
\({A}_{3}\) | (0.44, 0.51) (0.43, 0.49) | (0.15, 0.84) (0.14, 0.81) | 3.91 |
\({A}_{4}\) | (0.40, 0.45) (0.48, 0.59) | (0.16, 0.78) (0.07, 0.87) | 4.89 |
\({A}_{5}\) | (0.48, 0.56) (0.44, 0.50) | (0.12, 0.77) (0.16, 0.81) | 4.27 |
\({A}_{6}\) | (0.44, 0.47) (0.45, 0.37) | (0.18, 0.82) (0.19, 0.80) | 3.14 |
Comparative investigation—proposed vs. other models
Factors | PHFS-based decision models | ||||
---|---|---|---|---|---|
Proposed | [23] | [27] | [31] | [37] | |
Preference information | PHFI | ||||
Missing entry in matrices | Considered in this work | Assumed to be fully filled – practically not true | |||
Imputation | Done methodically | Not imputed | |||
Weights of criteria | Calculated – Mathematical model | Directly assigned | Calculated – Best worst approach | Directly assigned | Calculated – Choquet integral |
Weights of experts | Calculated – Mathematical model | Not calculated | |||
Partial information | Effectively utilized | No provision to use | |||
Preference aggregation | Done using Hamy mean | Prioritized operator | n/a | ||
Ranking | COPRAS | Aggregation operator | Dominance measure | Regret theory | TODIM |
Order | \({A}_{2}\succ {A}_{4}\succ {A}_{1}\succ {A}_{5}\succ {A}_{3}\succ {A}_{6}\) | \({A}_{4}\succ {A}_{1}\succ {A}_{2}\succ {A}_{5}\succ {A}_{3}\succ {A}_{6}\) | \({A}_{2}\succ {A}_{1}\succ {A}_{4}\succ {A}_{5}\succ {A}_{3}\succ {A}_{6}\) | \({A}_{2}\succ {A}_{4}\succ {A}_{5}\succ {A}_{1}\succ {A}_{3}\succ {A}_{6}\) | \({A}_{2}\succ {A}_{1}\succ {A}_{4}\succ {A}_{5}\succ {A}_{3}\succ {A}_{6}\) |