A THEORY OF QUALITATIVE SIMILARITY

Klaus Nehring, Gordon H. Hanson and Humberto G. Llavador
Additional contact information
Humberto G. Llavador: Department of Economics, University of California Davis

No 85, Working Papers from University of California, Davis, Department of Economics

Abstract: The central result of this paper establishes an isomorphism between two types of mathematical structures: ""ternary preorders"" and ""convex topologies."" The former are characterized by reflexivity, symmetry and transitivity conditions, and can be interpreted geometrically as ordered betweenness relations; the latter are defined as intersection-closed families of sets satisfying an ""abstract convexity"" property. A large range of examples is given. As corollaries of the main result we obtain a version of Birkhoff''s representation theorem for finite distributive lattices, and a qualitative version of the representation of ultrametric distances by indexed taxonomic hierarchies.

Pages: 29
Date: 2003-01-07
References: Add references at CitEc
Citations:

Downloads: (external link)
https://repec.dss.ucdavis.edu/files/o5HxDtphgKZ4QsobhzGz4U72/97-10.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cda:wpaper:85

Access Statistics for this paper

More papers in Working Papers from University of California, Davis, Department of Economics Contact information at EDIRC.
Bibliographic data for series maintained by Letters and Science IT Services Unit ().