Orderings of Opportunity Sets
We consider an extension of the class of multi-utility hyper-relations, the class of semidecent hyper-relations. A semi-decent hyper-relation satisfies monotonicity, stability with respect to contraction, and the union property. We analyze the class of semi-decent hyper-relations both associating them to an appropriate class of choice functions and considering decomposition of a decent relations via 'elementary' ones. Doing so, we consider images in the set of choice functions of three subclasses of semi-decent hyper-relations: the decent hyper-relations, the transitive decent hyper-relations , and transitive decent hyper-relations which satisfy the condition LE of lattice equivalence. We prove that the image of the set of decent hyper-relations coincides with of the set of heritage choice functions; the image of the set of transitive decent hyper-relations coincides with the set of closed choice functions; the image of the set of transitive decent hyper-relations which satisfy the LE coincides with the set of Plott functions. We consider, for each of the above subclasses of hyper-relations, the problem of the decomposition of a given hyper-relation into `elementary' ones, namely the representation of a given hyper-relation as the intersection of `elementary'ones.
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- Bernard Monjardet & Raderanirina Vololonirina, 2004.
"Lattices of choice functions and consensus problems,"
Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers)
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- Domenach, Florent & Leclerc, Bruno, 2004. "Closure systems, implicational systems, overhanging relations and the case of hierarchical classification," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 349-366, May.
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