The duality between the anti-exchange closure operators and the path independent choice operators on a finite set

DOI10.1016/S0165-4896(00)00061-5zbMath0994.91012MaRDI QIDQ5932330

Vololonirina Raderanirina, Bernard Monjardet

Publication date: 7 May 2001

Published in: Mathematical Social Sciences (Search for Journal in Brave)

zbMATH Keywords

closure operatorchoice functionchoice operatorrevealed preference

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Social choice (91B14)

Related Items (21)

The lattices of closure systems, closure operators, and implicational systems on a finite set: A survey ⋮ SOME ORDER DUALITIES IN LOGIC, GAMES AND CHOICES ⋮ Extreme point axioms for closure spaces ⋮ Mixture sets on finite domains ⋮ Resolutions of convex geometries ⋮ A discrete duality between nonmonotonic consequence relations and convex geometries ⋮ Maximal closed set and half-space separations in finite closure systems ⋮ Convex rough sets on finite domains ⋮ Convexity in ordered matroids and the generalized external order ⋮ Statement of precedence and a comment on IIA terminology ⋮ The presence of lattice theory in discrete problems of mathematical social sciences. Why. ⋮ Transformations of discrete closure systems ⋮ Mathematics of Plott choice functions ⋮ Path-independence and closure operators with the anti-exchange property ⋮ The affine representation theorem for abstract convex geometries ⋮ Duality between quasi-concave functions and monotone linkage functions ⋮ A new characterization of the path independent choice functions ⋮ Krein-Milman spaces ⋮ Going down in (semi)lattices of finite moore families and convex geometries ⋮ Violator spaces vs closure spaces ⋮ Substitutable choice functions and convex geometry

Cites Work

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