A mathematical perspective for software measure research

We identify and analyse basic principles which necessarily underlie software measures research. In the prevailing paradigm for the validation of software measures, there is a fundamental assumption that the sets of measured documents are ordered and that measures should report these orders. We describe mathematically the nature of such orders. Consideration of these orders suggests a hierarchy of software document measures, a methodology for developing new measures and a general approach to the analytical evaluation of measures. We also point out the importance of units for any type of measurement and stress the perils of equating document structure complexity and psychological complexity.