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Bi-cooperative games have been introduced by Bilbao as a generalization of classical cooperative games, where each player can participate positively to the game (defender), negatively (defeater), or do not participate (abstentionist). In a voting situation (simple games), they coincide with...
Persistent link: https://www.econbiz.de/10005510656
Bi-cooperative games were introduced by Bilbao et al. as a generalization of TU cooperative games, in which each player can participate positively, negatively, or not at all. In this paper, we propose a definition of a share of the worth obtained by some players after they decided on their...
Persistent link: https://www.econbiz.de/10010738682
Bi-cooperative games have been introduced by Bilbao as a generalization of classical cooperative games, where each player can participate positively to the game (defender), negatively (defeater), or do not participate (abstentionist). In a voting situation (simple games), they coincide with...
Persistent link: https://www.econbiz.de/10010750669
We study in this paper the notion of conditional relative importance in a quantitative framework. Bi-capacities are shown to be suitable to represent such notion. We restrict ourself to the case when the relative importance of two criteria are conditional on a third being attractive or...
Persistent link: https://www.econbiz.de/10010750700
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
We are interested in modeling interaction between criteria in Multi-Criteria Decision Making when underlying scales are bipolar. Interacting phenomena involving behavioral bias between attractive and repulsive values are in particular considered here. We show in an example that both the Choquet...
Persistent link: https://www.econbiz.de/10010750754
The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a...
Persistent link: https://www.econbiz.de/10010750818
We present in this paper necessary and sufficient conditions for the representation of preferences in a decision making problem, by the Sugeno integral, in a purely ordinal framework. We distinguish between strong and weak representations.
Persistent link: https://www.econbiz.de/10010750963
Persistent link: https://www.econbiz.de/10005337676
Persistent link: https://www.econbiz.de/10005347171