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• W2018696312 abstract "Bi-capacities arise as a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wide variety of decision behaviours, encompassing models such as cumulative prospect theory (CPT). The aim of this paper in two parts is to present the machinery behind bi-capacities, and thus remains on a rather theoretical level, although some parts are firmly rooted in decision theory, notably cooperative game theory. The present first part is devoted to the introduction of bi-capacities and the structure on which they are defined. We define the Möbius transform of bi-capacities, by just applying the well-known theory of Möbius functions as established by Rota to the particular case of bi-capacities. Then, we introduce derivatives of bi-capacities, by analogy with what was done for pseudo-Boolean functions (another view of capacities and set functions), and this is the key point to introduce the Shapley value and the interaction index for bi-capacities. This is done in a cooperative game theoretic perspective. In summary, all familiar notions used for fuzzy measures are available in this more general framework." @default.
• W2018696312 created "2016-06-24" @default.
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• W2018696312 date "2005-04-01" @default.
• W2018696312 modified "2023-10-17" @default.
• W2018696312 title "Bi-capacities—I: definition, Möbius transform and interaction" @default.
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• W2018696312 doi "https://doi.org/10.1016/j.fss.2004.08.012" @default.
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