  Fractional graph isomorphism is the linear relaxation of an integer
programming formulation of graph isomorphism. It preserves some invariants of
graphs, like degree sequences and equitable partitions, but it does not
preserve others like connectivity, clique and independence numbers, chromatic
number, vertex and edge cover numbers, matching number, domination and total
domination numbers.
  In this work, we extend the concept of fractional graph isomorphism to
hypergraphs, and give an alternative characterization, analogous to one of
those that are known for graphs. With this new concept we prove that the
fractional packing, covering, matching and transversal numbers on hypergraphs
are invariant under fractional hypergraph isomorphism. As a consequence,
fractional matching, vertex and edge cover, independence, domination and total
domination numbers are invariant under fractional graph isomorphism. This is
not the case of fractional chromatic, clique, and clique cover numbers. In this
way, most of the classical fractional parameters are classified with respect to
their invariance under fractional graph isomorphism.
