Closure operators and choice operators: a survey

Bernard Monjardet

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Abstract: In this talk I will give a overview on the connections between closure operators and choice operators and on related results. An operator on a finite set S is a map defined on the set P(S) of all the subsets of S. A closure operator is an extensive, isotone and idempotent operator. A choice operator c is a contracting operator (c(A) ⊆ A, for every A ⊆ S). Choice operators and their lattices have been very studied in the framework of the theory of the revealed preference in economics. A significant connection between closure operators and choice operators is the duality between anti-exchange operators (corresponding to convex geometries) and path-independent choice operators. More generally, there is a one-to-one correspondence between closure operators and choice operators.

Keywords: : choice function; closure operator; convex geometry; duality; lattice; path-independence; revealed preference; dualité; fermeture; fonction de choix; géométrie convexe; indépendance du chemin; préférence révélée; treillis (search for similar items in EconPapers)
Date: 2007-10-24
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Published in CLA 2007 Fifth International Conference on Concept Lattices and Their Applications, Oct 2007, Montpelleir, France

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