Communicative Approximations as Rough Sets

Introduction: Communicative approximations are equivalence relations. For considering Communicative approximation, new constructs are necessary including “rough points” and “rough intervals”. “Communication about quantities is defined on a shared conventional space, which constitutes a tessellation on the real number line”. The uncertainty which results from measurement error (±η) is defined on a tolerance approximation spate whereas error reflected in communication (€) is defined on the communicative approximation space. In order to avoid a false impression of greater precision we assume that € ≥ ±η. The worst case arises when €=±η. The approximation space is defined as the domain of discourse, together with an equivalence relation on it.