On the foundations of measurement

By J. Barzilai. 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236), 2001

645 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3004b3396724117b88913f85df51d5708a385835

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Citations in the corpus

Software Engineering Metrics: What Do They Measure and How Do We Know? (2004, background): “[17, p. 29-30] The representational theory is laid out generally in [6] [10] [11] and harshly critiqued by Michell [18].”
Measurement: A Very Short Introduction—Rejoinder to discussion (2016, background): “I have in mind books such as the 3-volume work, Krantz et al. (1971); Suppes et al. (1989); Luce et al. (1990); or the book by Roberts (1979); or indeed my own earlier technical book Measurement Theory and Practice (MTAP) mentioned earlier.”
A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid (2008, background): “More generally, when F is any increasing function from Sn to S, equation (2.1) is the so-called decomposable model of measurement theory (Krantz et al., 1971), and F is called an aggregation function.”
Is Construct Validation Valid? (2016, background): “is a demonstrated homomorphism between an observable relation and a numerical relational structure (Krantz et al. 1971).”
A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package (2008, background): “[3, 4] in which U is defined by U(x) := F (u1(x1), .”
An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria (2000, background): “[14]), that is, an homomorphism xi : A → IR defined up to a positive linear transformation φi(xi) = ri xi + si with ri > 0.”
The Rise of non-Archimedean Mathematics and the Roots of a Misconception I: The Emergence of non-Archimedean Systems of Magnitudes (2006, background): “…while lacking elegance, is entirely adequate to the task at hand and constitutes, in our opinion, sufficient reason for regarding Stolz as the father of the modern theory of extensive magnitudes, an honor usually conferred on Helmholtz [1887] or Hölder [1901] (cf. [Krantz et al. 1971, p. 71]).”
Towards Meaningful Statements in IR Evaluation: Mapping Evaluation Measures to Interval Scales (2021, background): “introduction to the representational measurement theory [53, 59, 87], clearly explaining why (or why not) certain operations and significance tests should be permissible on a given scale and presenting the different stances on this long-standing debate;”
Accounting, empirical measurement and intellectual capital (2001, neutral): “# MCB University Press, 1469-1930”
Frontiers of test validity theory: measurement, causation, and meaning (2014, positive): “The representational theories (Krantz et al., 1971) are more flexible than the classical theory (which assumes a ratio scale), because they allow for different kinds of empirical relational systems and different kinds of numerical systems (e.g. ordinal), but they are still very difficult to…”