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 analysis of modeled behaviuors needs complex analytic tools. In this paper we propose a process algebraic approach to specification and analysis of fuzzy behaviours. Indeed, we introduce a Fuzzy variant of CCS (Calculus of Communicating Processes), that permits compositionally describing fuzzy behaviours. Moreover, we also show how standard process algebra formal tools, like modal logics and behavioural equivalences, can be used for supporting fuzzy reasoning. Keywords— Fuzzy Systems, Process Algebras, Compositional Fuzzy Reasoning