Extending the Choquet integral

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Extending 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 treated as an additive function taking values on subsets itself: the value associated with each subset is simply the sum of the values associated with all the atoms (or 1-cardinal subsets) in that subset. The Choquet technique is here extended to the case where the integrand, just like the measure, is a nonadditive function taking values on subsets itself. The resulting aggregation operator is an extension of the Choquet integral: the former coincides with the latter whenever the integrand is additive. Four such extensions are provided, two of which are obtained by means of the M¨obius inversion of ...
Giovanni Rossi
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2007
Authors Giovanni Rossi
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