ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 65, 2 (1996)
pp. 195-214

ON THE ORDER-COMPLETION OF ADDITIVE CONJOINT STRUCTURES
F. VOGT

Abstract. Measurement theory provides additive conjoint structures for additive representations of empirical data. Roughly, an additive conjoint structure is a product of (quasi)ordered sets with some properties connecting the different factors of the product. Well-known Debreu's Theorem says that every additive conjoint structure can be embedded in a vector space over the real numbers. This embedding yields a completion of the additive conjoint structure where every factor becomes a complete lattice. This paper introduces a synthetical way of constructing this completion without using real numbers.

AMS subject classification.
Keywords. additive conjoint structure, measurement theory, Dedekind-MacNeille Completion, Formal Concept Analysis, Debreu's Theorem, Thomsen Condition, solvability conditions, synthetical geometry

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Acta Mathematica Universitatis Comenianae
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