Bipartite Matching with Incomplete Ordinal Relations Considering Matching Aspirations

Background: A new methodology is developed for bipartite matching decision, in which preferences of the agents from two sides are incomplete ordinal relations and matching aspirations. The bipartite matching problem with incomplete ordinal relations and matching aspirations is firstly provided. Methods: In the presented methodology, the incomplete ordinal relations are translated to the incomplete Borda counting matrixes, and matching aspirations are determined based on theory analysis. According to the incomplete Borda counting matrixes, the matching aspiration matrix, a bipartite matching model under the condition of one-to-one matching is developed. Results: The bipartite matching scheme can be obtained by solving the matching model. Conclusion: In the end, an example is used to illustrate the application of the presented methodology.