The authors are employing some of their previous works in structural acoustics to define, investigate, and interpret the response behaviors of so called fuzzy structures. A formalism is developed to describe the response behavior of a master structure to which an ensemble of appendages are attached. The impulse response function for the master structure is, ad hoc, assumed to be proper and known. The appendages are assumed to be described by an impedance operator composed of individual impedances that are localized; each impedance is stated in terms of a singular position and an associated impedance. An impulse response function is then derived and is shown to be proper. The propriety of the impulse response function demands that it be dependent only on quantities and parameters that describe the appended master structure; it needs to be independent of the in situ response of the structure and the external drive that generates the response. Models of naturally interacting and artificially noninteracting appendages on a master structure yield impulse response functions that obey the Le Chatelier’s principle. A model based on the Born approximation violates this principle and, therefore, its use is highly limited. All three models are employed to explain the notion of a configuration for the disposition of an ensemble of appendages. A configuration is shown to require the specification of a two-vector set comprising the positions and impedances of the appendages. The notion of an ensemble of configurations is then proposed to define deviations from a prime configuration. Configurational averages of the equation of motion of the appended master structure can then be performed exposing the averaged response behavior for this structure. An ensemble of appendages that can be assigned an ensemble of configurational deviations that are defined statistically is dubbed fuzzy (structural fuzzy). In turn, a statistical ensemble of configurations about a prime configuration of appendages on a master structure defines a fuzzily appended master structure.