A process Algebra Approach to Fuzzy Reasoning

Fuzzy systems address the imprecision of the input and output variables, which formally describe notions like "rather warm" or "pretty cold", while provide a behaviour that depends on fuzzy data. This class of systems are classically represented by means of Fuzzy Inference Systems (FIS), a computing framework based on the concepts of fuzzy if-then rules and fuzzy reasoning. Even if FIS are largely used, these lack in compositionality. Moreover, the analy- sis of modeled behaviuors needs complex analytic tools. In this paper we propose a process algebraic approach to specification and analy- sis of fuzzy behaviours. Indeed, we introduce a Fuzzy variant of CCS (Calculus of Communicating Processes), that permits composition- ally describing fuzzy behaviours. Moreover, we also show how stan- dard process algebra formal tools, like modal logics and behavioural equivalences, can be used for supporting fuzzy reasoning.