Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Conditions Equivalent to Unit Representations of Ordered Relational Structures.

R. Duncan Luce1

  • 1Institute for Mathematical Behavioral Sciences, University of California, Irvine

Journal of Mathematical Psychology
|February 17, 2001
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Reduction Invariance and Prelec's Weighting Functions.

Journal of mathematical psychologyยท2001
See all related articles

This study explores automorphism subgroups in ordered structures, finding conditions for numerical representations. These conditions, including homogeneous and Archimedean properties, are shown to be sufficient for specific scale types.

Area of Science:

  • Order theory
  • Group theory
  • Mathematical structures

Background:

  • Investigates subgroups of automorphisms in linearly ordered relational structures.
  • Connects properties of automorphism groups to numerical representations of structures.

Purpose of the Study:

  • To identify conditions equivalent to translations forming a homogeneous, Archimedean ordered group.
  • To establish sufficiency of necessary conditions for numerical representation.

Main Methods:

  • Analysis of automorphism subgroups and their induced asymptotic order.
  • Examination of homogeneity, Archimedean properties, and convex subgroups.

Main Results:

  • Theorem 5: Connected asymptotic order, homogeneity, Archimedean translations, and relative Archimedean dilations are sufficient for numerical representation.

Related Experiment Videos

  • Identifies the condition for dilations being Archimedean relative to all automorphisms.

    • Conclusions:

    • The established conditions are sufficient for numerical representations between interval and ratio scales.
    • Results do not simplify proofs for Dedekind complete cases; parallel automorphisms are also examined.