منابع مشابه
Bi-capacities -- Part II: the Choquet integral
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 as Cumulative Prospect Theory (CPT). The aim of this paper in two parts is to present the machinery behind bicapacities, and thus remains on a rather theoretical ...
متن کاملThe Choquet integral for 2-additive bi-capacities
Bi-capacities have been presented recently by the authors as a natural generalization of capacities (fuzzy measures). Usual concepts as Möbius transform, Shapley value and interaction index, Choquet integral, kadditivity can be generalized. We present formulas of the Choquet integral w.r.t. the Möbius transform, and w.r.t. the interaction index for 2-additive bi-capacities.
متن کاملExtending the Choquet integral
In decision under uncertainty, the Choquet integral yields the expectation of a random variable with respect to a fuzzy measure (or non-additive probability or capacity). In general, for the discrete setting, this technique allows to integrate functions taking values on a finite n-set with respect to a (fuzzy) measure taking values on subsets of such a set. Yet, the integrand may well be treate...
متن کاملThe bipolar Choquet integral representation
Cumulative Prospect Theory of Tversky and Kahneman (1992) is the modern version of Prospect Theory (Kahneman and Tversky (1979)) and is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e. the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assu...
متن کاملTwofold integral and multi-step Choquet integral
In this work we study some properties of the twofold integral and, in particular, its relation with the 2-step Choquet integral. First, we prove that the Sugeno integral can be represented as a 2-step Choquet integral. Then, we turn into the twofold integral studying some of its properties, establishing relationships between this integral and the Choquet and Sugeno ones and proving that it can ...
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ژورنال
عنوان ژورنال: Fuzzy Sets and Systems
سال: 2005
ISSN: 0165-0114
DOI: 10.1016/j.fss.2004.08.013