Three-Sided Fuzzy Stable Matching Problem Based on Combination Preference

Previous studies, constrained by the overly rigid stability requirements, often fail to adapt to complex systems and struggle to identify stable outcomes that align with the practical context of multi-agent resource allocation. To address the three-sided matching problem in complex socio-technical and business management systems, this paper proposes a fuzzy stable matching method for three-sided agents under a framework of combinatorial preference relations, integrating network and decision theory. First, we construct a membership function to measure the degree of preference satisfaction between elements of different agents, and then define the concept of fuzzy stability. By incorporating preference satisfaction, we introduce the notion of fuzzy blocking strength and derive the generation conditions for blocking triples and fuzzy stability under the fuzzy stable criterion. Furthermore, we abstract the three-sided matching problem with combined preference relations into a shortest path problem. Second, we prove the equivalence between the shortest path solution and the stable matching outcome. We adopt Dijkstra’s algorithm for problem-solving and derive the time complexity of the algorithm under the pruning strategy. Finally, we apply the proposed model and algorithm to a case study of project assignment in software companies, thereby verifying the feasibility and effectiveness of this three-sided matching method. Compared with existing approaches, the fuzzy stable matching method developed in this study demonstrates distinct advantages in handling preference uncertainty and system complexity. It provides a more universal theoretical tool and computational approach for solving flexible resource allocation problems prevalent in real-world scenarios.