There are recent attempts to address some of these issues by using alternative characterizations of word meaning that do not involve creating a partition of usages into senses (McCarthy and Navigli 2009;Erk, McCarthy, and Gaylord 2013), and by asking WSI systems to produce soft or graded clusterings (Jurgens and Klapaftis 2013) where tokens can belong to a mixture of the clusters.
these approaches do not overtly consider the location of a lemma on the continuum, but doing so should help in determining an appropriate representation.