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. 2025 Jul 2;15(1):22902.
doi: 10.1038/s41598-025-00388-6.

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

Xiaohua Liu  1 , Qi Yue  2 , Bin Hu  3 , Yuan Tao  4
Affiliations

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

Xiaohua Liu et al. Sci Rep. .

Abstract

In view of the lack of research on graduate students and supervisors matching (GSSM) decision-making, this study proposes a novel many-to-one matching decision-making method for graduate students and supervisors (GSS) considering conformity psychology and graduate students' preferences from a stability-based fairness perspective. First, the many-to-one matching problem for GSS is described. To tackle this problem, linguistic term matrices (LTMs) provided by bilateral subjects are transformed into Pythagorean fuzzy matrices (PFMs). On the one hand, according to the transference relation of graduate students, a conformity coefficient matrix is built. Then a PFM considering conformity psychology is established. Attribute weight vectors adjusted by conformity coefficients are formulated based on comparison information of graduate students and the conformity coefficient matrix. On this basis, a comprehensive PFM of graduate students is constructed. On the other hand, a preference coefficient matrix of graduate students is built by using TODIM (a Portuguese acronym for interactive and multicriteria decision making). And a PFM considering graduate students' preferences is constructed. Attribute weight vectors of supervisors are determined based on attribute comparison information. On this basis, a comprehensive PFM of supervisors is set up. Furthermore, satisfaction matrices of GSS are constructed by using TOPSIS (technique for order preference by similarity to the ideal solution) and grey correlation degrees. A many-to-one GSSM model considering stability-based fairness is established by introducing matching matrix and stable matching matrix. The many-to-one matching model is then transformed into a one-to-one matching model by introducing virtual supervisor subjects; the optimal matching scheme between GSS is obtained by solving the above model. Finally, the feasibility, effectiveness and innovation of the proposed method are verified by an example analysis. The key findings of this study are listed as follows: (1) A new score of Pythagorean fuzzy numbers (PFNs) is proposed. (2) A method for converting linguistic term sets (LTSs) into PFNs is developed. (3) A weight calculation that combines conformity psychology with BWM is improved. (4) A novel method for satisfaction calculation considering conformity psychology and graduate students' preferences is introduced. (5) A GSSM model considering stability-based fairness is built.

Keywords: Conformity psychology; Graduate students and supervisors matching decision-making; Many-to-one matching; Pythagorean fuzzy environment; Stability-based fairness.

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Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
Solution idea for many-to-one GSSM decision-making considering stability-based fairness.
Algorithm 1
Algorithm 1
Construction of the PFM formula image considering conformity psychology
Fig. 2
Fig. 2
Flowchart of Algorithm 1.
Algorithm 2
Algorithm 2
Calculation of attribute weight vectors formula image considering conformity coefficients
Fig. 3
Fig. 3
Flowchart of Algorithm 2.
Algorithm 3
Algorithm 3
Construction of satisfaction matrix formula image of graduate students
Fig. 4
Fig. 4
Flowchart of Algorithm 3.
Algorithm 4
Algorithm 4
Construction of PFM formula image considering graduate students’ preferences
Fig. 5
Fig. 5
Flowchart of Algorithm 4.
Algorithm 5
Algorithm 5
Calculation of attribute weight vectors formula image of supervisors
Fig. 6
Fig. 6
Flowchart of Algorithm 5.
Algorithm 6
Algorithm 6
Construction of satisfaction matrix formula image of supervisors
Fig. 7
Fig. 7
Flowchart of Algorithm 6.
Fig. 8
Fig. 8
Transference relation of graduate students.
Fig. 9
Fig. 9
Optimal matching scheme formula image based on grey correlation coefficient formula image.
Fig. 10
Fig. 10
Optimal matching scheme formula image based on weight vector formula image.
Fig. 11
Fig. 11
Comparative analysis based on different methods.
See this image and copyright information in PMC

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