  Formal methods are widely recognized as a powerful engineering method for the
specification, simulation, development, and verification of distributed
interactive systems. However, most formal methods rely on a two-valued logic,
and are therefore limited to the axioms of that logic: a specification is valid
or invalid, component behavior is realizable or not, safety properties hold or
are violated, systems are available or unavailable. Especially when the problem
domain entails uncertainty, impreciseness, and vagueness, the appliance of such
methods becomes a challenging task. In order to overcome the limitations
resulting from the strict modus operandi of formal methods, the main objective
of this work is to relax the boolean notion of formal specifications by using
fuzzy logic. The present approach is based on Focus theory, a model-based and
strictly formal method for componentbased interactive systems. The contribution
of this work is twofold: i) we introduce a specification technique based on
fuzzy logic which can be used on top of Focus to develop formal specifications
in a qualitative fashion; ii) we partially extend Focus theory to a fuzzy one
which allows the specification of fuzzy components and fuzzy interactions.
While the former provides a methodology for approximating I/O behaviors under
imprecision, the latter enables to capture a more quantitative view of
specification properties such as realizability.
