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Lattices of choice functions and consensus problems

Monjardet, Bernard; Vololonirina, Raderanirina - HAL - 2004

lattice, and we study the properties of these lattices. The lattice of choice functions satisfying (H) is distributive …, whereas the lattice of choice functions verifying (C) is atomistic and lower bounded, and so has many properties. On the … contrary, the lattice of choice functions satisfying(O) is not even ranked. Then using results of the axiomatic and metric …

Persistent link: https://www.econbiz.de/10010750440

A new approach to the core and Weber set of multichoice games

Grabisch, Michel; Xie, Lijue - HAL - 2007

Multichoice games have been introduced by Hsiao and Raghavan as a generalization of classical cooperative games. An important notion in cooperative game theory is the core of the game, as it contains the rational imputations for players. We propose two definitions for the core of a multichoice...

Persistent link: https://www.econbiz.de/10010750467

The multiple facets of the canonical direct implicational basis

Bertet, Karell; Monjardet, Bernard - HAL - 2005

, artificial intelligence, logical programming or lattice theory. Implicational systems represents an efficient and convenient tool …

Persistent link: https://www.econbiz.de/10010750697

Capacities and Games on Lattices: A Survey of Result

Grabisch, Michel - HAL - 2006

We provide a survey of recent developments about capacities (or fuzzy measures) and ccoperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations...

Persistent link: https://www.econbiz.de/10010750699

Bipolarization of posets and natural interpolation

Grabisch, Michel; Labreuche, Christophe - HAL - 2008

The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of $[0,1]^n$. We take this basic fact as a starting point to define the Choquet integral in a very general way, using the geometric realization of lattices and their...

Persistent link: https://www.econbiz.de/10010750727

Games on lattices, multichoice games and the Shapley value: a new approach

Grabisch, Michel; Lange, Fabien - HAL - 2007

Persistent link: https://www.econbiz.de/10010750952

Stability and Index of the Meet Game on a Lattice

Abdou, Joseph - HAL - 2012

We study the stability and the stability index of the meet game form defined on a meet semilattice. Given any active coalition structure, we show that the stability index relative to the equilibrium, to the beta core and to the exact core is a function of the Nakamura number, the depth of the...

Persistent link: https://www.econbiz.de/10011026051

Stability and Index of the Meet Game on a Lattice

Abdou, Joseph - HAL - 2010

We study the stability and the stability index of the meet game form defined on a meet-semilattice. Given any active coalition structure, we show that the stability index relative to the equilibrium, to the beta core and to the exact core is a function of the Nakamura number, the depth of the...

Persistent link: https://www.econbiz.de/10010603656

Stability and Index of the Meet Game on a Lattice

Abdou, Joseph - HAL - 2011

Persistent link: https://www.econbiz.de/10010610165

The lattice structure of the S-Lorenz core

Iehlé, Vincent - HAL - 2014

the Lorenz order, is a bounded join semi-lattice. Furthermore the set admits as sublattice the S-Lorenz core intersected …

Persistent link: https://www.econbiz.de/10010899299