A Theory of Qualitative Similarity
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.
Year of publication: |
1997
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Authors: | Nehring, Klaus ; Hanson, Gordon H. ; Llavador, Humberto G. |
Publisher: |
Davis, CA : University of California, Department of Economics |
Saved in:
freely available
Series: | Working Paper ; 97-10 |
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Type of publication: | Book / Working Paper |
Type of publication (narrower categories): | Working Paper |
Language: | English |
Other identifiers: | hdl:10419/189458 [Handle] RePEc:cda:wpaper:97-10 [RePEc] |
Source: |
Persistent link: https://www.econbiz.de/10011940943
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