A probabilistic theory of measurement

Measurability invariance, continuity and a portfolio representation

“…In two significant papers, Rossi [1] and Rossi [15], established a framework to assess measurability in both a deterministic and probabilistic setting. In this paper, we have extended that framework to include a set of invariance and continuity conditions which a measure should satisfy.…”

“…Rossi [15] examines the limitations of representational measurement theory, which he considers to be restricted by two factors; first, the inability to account for uncertainty, secondly the lack of specification of the measuring system. Rossi specifies two frameworks for measurement, a deterministic framework and a probabilistic framework.…”

Algebraic approach to extensive measurement based on direct comparison

“…[2,3]) and papers (see e.g. [6]). GUIDE [1] recommends the unification the error theory in the framework of statistical approach, but this leads to the randomisation of the systematic components.…”

Measurability

“…From a theoretical standpoint, at least if we consider a finite set of objects A, we may answer that they are both necessary and sufficient, since we could think of examining all the elements in A and assigning a number to all of them, in such a way as to respect (reproduce) their empirical relations [30]. Yet this is not the way measurement takes place and so we have requested, in the proposed reference procedure, to have at least one fully devised measurement procedure.…”

“…In Ref. [30] we have proposed one such probabilistic framework, that may also be useful for addressing data processing in practical cases. As this topic is at present in its infancy, much more research effort may be envisaged in the future.…”