Computing uncertainty with uncertain numbers

A computational method for processing measurement data is discussed that applies the law of propagation of uncertainty, which is described in the Guide to the Expression of Uncertainty in Measurement. The method introduces the notion of an ‘uncertain number’, which is an entity that encapsulates information about the value and uncertainty of a quantity. Basic mathematical operations can be defined for uncertain numbers so that relationships between quantities can be expressed in a familiar way. Uncertain number equations can be arbitrarily combined, or decomposed into expressions for intermediate results, providing flexibility and convenience for automatic data processing while rigorously supporting uncertainty propagation. A geometrical description of simple uncertain number operations is also given.