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 ...

• Type: Conference
• Year: 2007
• Where: EUSFLAT
• Authors: Giovanni Rossi
• Keywords: Choquet Integral, EUSFLAT 2007, Function Taking Values, Integrand