Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  deal with the problem of how to extend a preference relation#R##N#over a set X of “objects” to the set of all subsets of X. This problem has been#R##N#carried out in the tradition of the literature on extending an order on a set to#R##N#its por set with the objective to analyze the axiomatic structure of families#R##N#of rankings over subsets. In particular, most of these approaches make use#R##N#of axioms aimed to prevent any kind of interaction among the objects in X.#R##N#,  apply coalitional games to study the problem of extending preferences over a finite set X to its por set 2 X . A coalitional game can#R##N#be seen as a numerical representation of a preference extension on 2 X .  focus on a particular class of extensions on 2 X such that the ranking induced#R##N#by the Shapley value of each coalitional game representing an extension in#R##N#this class, coincides with the original preference on X.#R##N#Some properties of Shapley extensions are discussed, with the objective to#R##N#justify and contextualize the application of Shapley extensions to the problem of ranking sets of possibly interacting objects.
['Stefano Moretti', 'Alexis Tsoukiàs']
I am writing a research paper on a idea Ranking Sets of Possibly Interacting Objects Using Shapley Extensions
[{"from": "human", "value": "I am writing a research paper on a idea Ranking Sets of Possibly Interacting Objects Using Shapley Extensions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  deal with the problem of how to extend a preference relation#R##N#over a set X of \u201cobjects\u201d to the set of all subsets of X. This problem has been#R##N#carried out in the tradition of the literature on extending an order on a set to#R##N#its por set with the objective to analyze the axiomatic structure of families#R##N#of rankings over subsets. In particular, most of these approaches make use#R##N#of axioms aimed to prevent any kind of interaction among the objects in X.#R##N#,  apply coalitional games to study the problem of extending preferences over a finite set X to its por set 2 X . A coalitional game can#R##N#be seen as a numerical representation of a preference extension on 2 X .  focus on a particular class of extensions on 2 X such that the ranking induced#R##N#by the Shapley value of each coalitional game representing an extension in#R##N#this class, coincides with the original preference on X.#R##N#Some properties of Shapley extensions are discussed, with the objective to#R##N#justify and contextualize the application of Shapley extensions to the problem of ranking sets of possibly interacting objects."}]