The Medical Treatment Service Matching Based on the Probabilistic Linguistic Term Sets with Unknown Attribute Weights


In multi-attribute two-sided matching (MATSM) problems, the attribute weights play an important role. The existing methods usually neglect the interaction and the effect among multiple attributes, resulting in irrational matching results. This paper takes this interaction into consideration. With the complexity of the matching environment, the uncertainties of agents should be considered. The probabilistic linguistic term set (PLTS) is a useful tool to describe the uncertainty and the limited cognition of agents. Thus, this paper aims to provide a novel MATSM method under the probabilistic linguistic environment with unknown attribute weights. Firstly, the attribute weights are determined by providing the probabilistic linguistic decision-making trial and evaluation laboratory (PL-DEMATEL) method. Besides, this paper constructs the gain and loss (GL) matrices and calculates the agents’ perceived values (PVs) by introducing prospect theory (PT). Then, the PVs are aggregated into the comprehensive PVs (CPVs) based on the obtained attribute weights. Next, this paper also proposes a ranking method, called probabilistic linguistic multi-attribute border approximation area comparison (PL-MABAC) method, to rank the multiple agents, which lay a solid foundation for stable matching constraint of the programming model. The matching results are obtained by solving the programming model. Finally, a case study of matching medical treatment service providers and demanders is presented to validate the proposed method. The comparative analyses and discussions are also provided to demonstrate its effectiveness.

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This study was funded by the National Natural Science Foundation of China (Nos. 71771155, 71571123), the scholarship under the UK–China Joint Research and Innovation Partnership Fund Ph.D. Placement Programme (CSC No. 201806240416) and the Teacher–Student Joint Innovation Research Fund of Business School of Sichuan University (No. H2018016).

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Correspondence to Zeshui Xu.



See Tables 11, 12, 13, 14, 15, 16, 17 and 18.

Table 11 The \(N_{i}\)
Table 12 The expectation provided by \(A_{i}\) for \(C_{{}}^{A}\)
Table 13 The evaluation of \(B_{j}\) for \(C_{{}}^{A}\)
Table 14 The expectation provided by \(B_{j}\) for \(C_{{}}^{B}\)
Table 15 The evaluation of \(A_{i}\) for \(C_{{}}^{B}\)
Table 16 The influence degree for \(C^{A}\) provided by \(A_{i}\)
Table 17 The influence degree for \(C^{B}\) provided by \(B_{j}\)
Table 18 The weight values

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Li, B., Zhang, Y. & Xu, Z. The Medical Treatment Service Matching Based on the Probabilistic Linguistic Term Sets with Unknown Attribute Weights. Int. J. Fuzzy Syst. 22, 1487–1505 (2020).

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  • Multiple-attribute two-sided matching
  • Probabilistic linguistic term sets
  • Decision-making trial and evaluation laboratory
  • Prospect theory
  • Multi-attributive border approximation area comparison