Before revision: For a many-to-one matching market where firms have strict and q-responsive preferences, we give a characterization of the  strongly stable fractional matching set as the union of the convex hull of  connected sets of stable matchings  .
After revision: For a many-to-one matching market where firms have strict and q-responsive preferences, we give a characterization of the strongly stable fractional matching set as the union of the convex hull of connected sets of stable matchings . Also, we prove that a strongly stable fractional matching is represented as a convex combination of stable matchings that are ordered in the common preferences of all firms .