Curt Holmer was always interested in the practical applications of statistical energy analysis, and the author had many discussions with him regarding its uses, and areas of transition to deterministic analysis. In some of the latest discussions, the topic of the ``mid-frequency range'' dominated, referred to by the author as ``the awkward zone.'' In this transition range between deterministic and fully probabilistic models, the greatest uncertainty may be in the joints---their actual location, and their rigidity. This suggests a hybrid approach, in which the substructures are treated as deterministic, and the joint locations and rigidities are uncertain, or in popular terms, fuzzy. This approach is exemplified by the joining of two plates by a link having a location and stiffness that are variable over a small range. The results of the analysis support such an approach, in that they show the kind of transition that has been noted in the awkward zone.