A survey of the most prominent definitions of zombie firms, together with their replication on a common dataset for euro area firms spanning the years 2004-2019, shows limited overlap and low comparability in the sets of firms identified by several prominent studies. Such low comparability raises the concern that these definitions are less capturing true zombie firms but rather financially vulnerable ones, and that the policy discourse may be misguided by statements on effectively distinct groups of firms. Thus, a formalization of the classifications of zombie firms is introduced which helps to make order in the growing number of variations and identification methodologies. Such formalization allows the concept of binary identification to be extended to that of fuzzy zombie identification, which allows quantification of a certain degree of "zombieness". A general procedure to turn arbitrary binary classifications into fuzzy ones is also presented and is shown to successfully increase consistency between zombie definitions.