Collective Decision Making under Qualitative Possibilistic Uncertainty : Principles and Characterization JURY
نویسندگان
چکیده
This Thesis raises the question of collective decision making under possibilistic uncertainty. We propose several collective qualitative decision rules and show that in the context of a possibilistic representation of uncertainty, the use of an egalitarian pessimistic collective utility function allows us to get rid of the Timing Effect. Making a step further, we prove that if both the agents’ preferences and the collective ranking of the decisions satisfy Dubois and Prade’s axioms (1995, 1998) and some additional axioms relative to collective choice, in particular Pareto unanimity, then the egalitarian collective aggregation is compulsory. The picture is then completed by the proposition and the characterization of an optimistic counterpart of this pessimistic decision rule. Our axiomatic system can be seen as an ordinal counterpart of Harsanyi’s theorem (1955). We prove this result in a formalism that is based on Von NeuMann and Morgenstern framework (1948) and compares possibilisitc lotteries. Besides, we propose a first attempt to provide a characterization of collective qualitative decision rules in Savage’s formalism; where decisions are represented by acts rather than by lotteries. From an algorithmic standpoint, we consider strategy optimization in possibilistic decision trees using the decision rules characterized in the first part of this work. So, we provide an adaptation of the Dynamic Programming algorithm for criteria that satisfy the property of monotonicity and propose a Multi-Dynamic programming and a Branch and Bound algorithm for those that are not monotonic. Finally, we provide an empirical comparison of the different algorithms proposed. We measure the execution CPU times that increases linearly according to the size of the tree and it remains affordable in average even for big trees. Then, we study the accuracy percentage of the approximation of the pertinent exact algorithms by Dynamic Programming: It appears that for U−max ante criterion the approximation of Multi-dynamic programming is not so good. Yet, this is not so dramatic since this algorithm is polynomial (and efficient in practice). However, for U+min ante decision rule the approximation by Dynamic Programming is good and we can say that it should be possible to avoid a full Branch and Bound enumeration to find optimal strategies.
منابع مشابه
Egalitarian Collective Decision Making under Qualitative Possibilistic Uncertainty: Principles and Characterization
This paper raises the question of collective decision making under possibilistic uncertainty; We study four egalitarian decision rules and show that in the context of a possibilistic representation of uncertainty, the use of an egalitarian collective utility function allows to get rid of the Timing Effect. Making a step further, we prove that if both the agents’ preferences and the collective r...
متن کاملAssessment of Green Supplier Development Programs by a New Group Decision-Making Model Considering Possibilistic Statistical Uncertainty
The assessment and selection of green supplier development programs are an intriguing and functional research subject. This paper proposes a group decision-making approach considering possibilistic statistical concepts under uncertainty to assess green supplier development programs (GSDPs) via interval-valued fuzzy sets (IVFSs). Possibility theory is employed to regard uncertainty by IVFSs. A n...
متن کاملA New Combination of Robust-possibilistic Mathematical Programming for Resilient Supply Chain Network under Disruptions and Uncertainty: A Real Supply Chain (RESEARCH NOTE)
Nowadays, the design of a strategic supply chain network under disruption is one of the most important priorities of the governments. One of the strategic purposes of managers is to supply the sustainable agricultural products and food in stable conditions which require the production of soil nutrients. In this regard, some disruptions such as sanctions and natural disasters have a destructive ...
متن کاملDécision collective sous incertitude possibiliste. Principes et axiomatisation
This paper raises the question of collective decision making under possibilistic uncertainty. We study several egalitarian decision rules and show that in the context of a possibilistic representation of uncertainty, the use of an egalitarian collective utility function allows us to get rid of the Timing Effect. Making a step further, we prove that if both the agents’ preferences and the collec...
متن کاملA possibilistic graphical model for handling decision problems under uncertainty
Possibilistic networks are important and efficient tools for reasoning under uncertainty. This paper proposes a new graphical model for decision making under uncertainty based on possibilistic networks. In possibilistic decision problems under uncertainty, available knowledge is expressed by means of possibility distribution and preferences are encoded by means another possibility distribution ...
متن کامل