Table 7 BPF matrix \(G^{\vartheta } = \left[ {g_{ij}^{\vartheta } } \right]_{8 \times 4}\) of graduate students for supervisors.

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

 

\(\chi_{1}\)

\(\chi_{2}\)

\(\gamma_{1}^{\vartheta }\)

\(\gamma_{2}^{\vartheta }\)

\(\gamma_{3}^{\vartheta }\)

\(\gamma_{4}^{\vartheta }\)

\(\gamma_{1}^{\vartheta }\)

\(\gamma_{2}^{\vartheta }\)

\(\gamma_{3}^{\vartheta }\)

\(\gamma_{4}^{\vartheta }\)

\(\vartheta_{1}\)

(0.76,0.53)

(0.75,0.56)

(0.61,0.55)

(0.56,0.53)

(0.8,0)

(0.62,0.54)

(0.57,0.62)

(0.79,0)

\(\vartheta_{2}\)

(0.51,0.7)

(0.76,0.57)

(0,0.86)

(0.5,0.63)

(0.65,0.55)

(0.62,0.54)

(0.57,0.62)

(0.8,0)

\(\vartheta_{3}\)

(0.68,0.56)

(0.59,0.57)

(0.62,0.55)

(0.79,0)

(0.57,0.53)

(0.71,0.52)

(0,0.55)

(0.64,0.54)

\(\vartheta_{4}\)

(0.68,0.57)

(0.76,0.58)

(0.62,0.56)

(0.79,0)

(0.66,0.56)

(0.77,0)

(0.58,0.79)

(0.52,0.62)

\(\vartheta_{5}\)

(0.81,0.63)

(0.74,0.69)

(0.6,0.82)

(0.71,0.63)

(0.78,0.62)

(0.65,0.61)

(0.69,0.77)

(0.77,0.6)

\(\vartheta_{6}\)

(0.84,0)

(0.63,0.61)

(0.57,0.72)

(0.73,0.55)

(0.56,0.66)

(0.72,0.55)

(0.6,0.8)

(0.67,0.57)

\(\vartheta_{7}\)

(0.67,0.59)

(0.84,0)

(0.56,0.81)

(0.63,0.58)

(0.7,0.61)

(0.67,0.6)

(0,0.87)

(0.64,0.57)

\(\vartheta_{8}\)

(0.54,0.65)

(0.53,0.69)

(0,0.86)

(0.72,0.52)

(0.73,0.53)

(0.5,0.63)

(0.57,0.62)

(0.73,0.51)

 

\(\chi_{3}\)

\(\chi_{4}\)

\(\gamma_{1}^{\vartheta }\)

\(\gamma_{2}^{\vartheta }\)

\(\gamma_{3}^{\vartheta }\)

\(\gamma_{4}^{\vartheta }\)

\(\gamma_{1}^{\vartheta }\)

\(\gamma_{2}^{\vartheta }\)

\(\gamma_{3}^{\vartheta }\)

\(\gamma_{4}^{\vartheta }\)

\(\vartheta_{1}\)

(0.59,0.71)

(0.8,0)

(0.62,0.55)

(0.8,0.59)

(0.53,0.55)

(0.63,0.54)

(0.54,0.71)

(0.7,0.62)

\(\vartheta_{2}\)

(0.84,0.59)

(0.8,0)

(0.71,0.44)

(0.71,0.63)

(0.47,0.67)

(0.71,0.51)

(0.54,0.56)

(0.71,0.63)

\(\vartheta_{3}\)

(0.74,0.62)

(0.73,0.51)

(0.59,0.5)

(0.79,0.59)

(0.45,0.74)

(0.63,0.54)

(0.66,0.51)

(0.79,0.59)

\(\vartheta_{4}\)

(0.75,0.63)

(0.65,0.55)

(0,0.68)

(0.55,0.8)

(0.6,0.59)

(0.78,0)

(0.56,0.57)

(0.58,0.73)

\(\vartheta_{5}\)

(0.93,0)

(0.72,0.63)

(0.77,0.55)

(0.88,0)

(0.59,0.73)

(0.66,0.61)

(0.66,0.71)

(0.89,0)

\(\vartheta_{6}\)

(0.86,0.62)

(0.61,0.55)

(0.62,0.64)

(0.67,0.64)

(0.62,0.61)

(0.66,0.57)

(0,0.79)

(0.67,0.63)

\(\vartheta_{7}\)

(0.87,0.65)

(0.76,0.57)

(0.75,0.51)

(0.83,0)

(0.7,0.61)

(0.74,0.57)

(0.61,0.63)

(0.83,0.66)

\(\vartheta_{8}\)

(0.74,0.62)

(0.65,0.54)

(0,0.69)

(0.63,0.6)

(0.48,0.67)

(0.72,0.51)

(0,0.79)

(0.7,0.62)

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