Table 17 Comparison results of different methods.

From: Graduate students and supervisors matching decision-making considering stability-based fairness based on TOPSIS and grey correlation degrees

Method

Optimal matching scheme \(\Upsilon^{ * }\)

The proposed method

\(\Upsilon_{1}^{ * } = \left\{ {\left( {\vartheta_{1} ,\chi_{2} } \right),\left( {\vartheta_{2} ,\chi_{2} } \right),\left( {\vartheta_{3} ,\chi_{1} } \right),\left( {\vartheta_{4} ,\chi_{2} } \right),\left( {\vartheta_{5} ,\chi_{3} } \right),\left( {\vartheta_{6} ,\chi_{4} } \right),\left( {\vartheta_{7} ,\chi_{1} } \right),\left( {\vartheta_{8} ,\chi_{4} } \right)} \right\}\)

Method I

\(\Upsilon_{7}^{ * } = \left\{ {\left( {\vartheta_{1} ,\chi_{2} } \right),\left( {\vartheta_{2} ,\chi_{2} } \right),\left( {\vartheta_{3} ,\chi_{1} } \right),\left( {\vartheta_{4} ,\chi_{1} } \right),\left( {\vartheta_{5} ,\chi_{3} } \right),\left( {\vartheta_{6} ,\chi_{4} } \right),\left( {\vartheta_{7} ,\chi_{2} } \right),\left( {\vartheta_{8} ,\chi_{4} } \right)} \right\}\)

Method II

\(\Upsilon_{1}^{ * } = \left\{ {\left( {\vartheta_{1} ,\chi_{2} } \right),\left( {\vartheta_{2} ,\chi_{2} } \right),\left( {\vartheta_{3} ,\chi_{1} } \right),\left( {\vartheta_{4} ,\chi_{2} } \right),\left( {\vartheta_{5} ,\chi_{3} } \right),\left( {\vartheta_{6} ,\chi_{4} } \right),\left( {\vartheta_{7} ,\chi_{1} } \right),\left( {\vartheta_{8} ,\chi_{4} } \right)} \right\}\)

Method III

\(\Upsilon_{8}^{ * } = \left\{ {\left( {\vartheta_{1} ,\chi_{2} } \right),\left( {\vartheta_{2} ,\chi_{2} } \right),\left( {\vartheta_{3} ,\chi_{2} } \right),\left( {\vartheta_{4} ,\chi_{1} } \right),\left( {\vartheta_{5} ,\chi_{3} } \right),\left( {\vartheta_{6} ,\chi_{4} } \right),\left( {\vartheta_{7} ,\chi_{1} } \right),\left( {\vartheta_{8} ,\chi_{4} } \right)} \right\}\)

Method IV

\(\Upsilon_{7}^{ * } = \left\{ {\left( {\vartheta_{1} ,\chi_{2} } \right),\left( {\vartheta_{2} ,\chi_{2} } \right),\left( {\vartheta_{3} ,\chi_{1} } \right),\left( {\vartheta_{4} ,\chi_{1} } \right),\left( {\vartheta_{5} ,\chi_{3} } \right),\left( {\vartheta_{6} ,\chi_{4} } \right),\left( {\vartheta_{7} ,\chi_{2} } \right),\left( {\vartheta_{8} ,\chi_{4} } \right)} \right\}\)

Method V

\(\Upsilon_{7}^{ * } = \left\{ {\left( {\vartheta_{1} ,\chi_{2} } \right),\left( {\vartheta_{2} ,\chi_{2} } \right),\left( {\vartheta_{3} ,\chi_{1} } \right),\left( {\vartheta_{4} ,\chi_{1} } \right),\left( {\vartheta_{5} ,\chi_{3} } \right),\left( {\vartheta_{6} ,\chi_{4} } \right),\left( {\vartheta_{7} ,\chi_{2} } \right),\left( {\vartheta_{8} ,\chi_{4} } \right)} \right\}\)

Method VI

\(\Upsilon_{7}^{ * } = \left\{ {\left( {\vartheta_{1} ,\chi_{2} } \right),\left( {\vartheta_{2} ,\chi_{2} } \right),\left( {\vartheta_{3} ,\chi_{1} } \right),\left( {\vartheta_{4} ,\chi_{1} } \right),\left( {\vartheta_{5} ,\chi_{3} } \right),\left( {\vartheta_{6} ,\chi_{4} } \right),\left( {\vartheta_{7} ,\chi_{2} } \right),\left( {\vartheta_{8} ,\chi_{4} } \right)} \right\}\)

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