|Autor(en):||Suck, R||Stichwörter:||(A,O)-structures; automorphism group; Business & Economics; Economics; Mathematical Methods In Social Sciences; Mathematics; Mathematics, Interdisciplinary Applications; order theory; Social Sciences, Mathematical Methods; WEAK ORDERS||Erscheinungsdatum:||1998||Herausgeber:||ELSEVIER SCIENCE BV||Journal:||MATHEMATICAL SOCIAL SCIENCES||Volumen:||36||Ausgabe:||2||Startseite:||91||Seitenende:||104||Zusammenfassung:||
This paper is concerned with structures of the form (A, 0) where A is a nonempty set and O a set of order relations on A. In particular we investigate their representability as a product structure with a weak order defined on a Cartesian product satisfying independence in the Conjoint Measurement sense. It is shown by a number of examples that systems of this kind, i.e. (A, B)-structures are often encountered. Conditions are formulated under which the set O can be partially ordered, which is a necessary requirement for its representability as a conjoint structure. The investigation of the relation between the automorphism group of (A, 0) and the automorphism group of the representing product structure gives rise to the introduction of a new class of automorphisms, generalizing the concept of a factorizable automorphism invented by Luce & Cohen. The generalized factorizable automorphisms are proven to form a group which contains the ordinary factorizable automorphisms as a normal subgroup. (C) 1998 Elsevier Science B.V. All rights reserved.
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