Compact Preference Representation via Fuzzy Constraints in Stable Matching Problems: Theoretical and Experimental Studies

The stable matching problem has many practical applications in two-sided markets, like those that assign doctors to hospitals or students to schools. Usually it is assumed that all agents in each side explicitly express a preference ordering over those in the other side. This can be unfeasible and impractical when the set of agents is very big. However, usually this set has a combinatorial structure, since each agent is often described by some features. To tackle these scenarios, we define a framework for stable matching problems where agents are allowed to express their preferences over those of the other group in a compact way, via soft constraints over the features describing these agents. We focus on a special kind of soft constraints, namely fuzzy constraints. We provide a solving engine for this new kind of stable matching problems that does not increase the time complexity of the classical Gale-Shapley algorithm, while maintaining stability of the matching returned. We then eval...