Towards a theoretical framework for measuring software attributes

Several attributes (e.g., size, complexity, cohesion, coupling) are commonly used in Software Engineering to refer to software product properties. A large number of measures have been proposed in the literature to measure these attributes. However, since software attributes are often defined in fuzzy and ambiguous ways, it is sometimes unclear whether the proposed measures are adequate for the software attributes they purport to measure (i.e., their construct validity). In recent years, a few approaches have been proposed to lay theoretical foundations for defining measures for software attributes, but no widespread agreement has been reached on a rigorous, unambiguous definition of software attributes. In this paper, we first extend previous work carried out on axiomatic approaches for the definition of measures for software attributes. Second, we show how a hierarchical axiomatic framework can be constructed to support the definition of consistent measures for a given attribute at different levels of measurement. This paper shows how axiomatic approaches can be combined with the theory of measurement scales so that, depending on the level of sophistication of our empirical understanding of the attribute, we can select an appropriate level of measurement and a suitable axiomatic framework.