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- Qualitative desintegrals as lower and upper possibilistic expectations doi link

Author(s): Dubois Didier, Prade Henri, Rico A.

Conference: 8th conference of the European Society for Fuzzy Logic and Technology (Milan, IT, 2013-09-11)
Proceedings: in proc. Eusflat, vol. p.. (2013)


DOI: 10.2991/eusflat.2013.51
Abstract:

Any capacity (i.e., an increasing set function) has been proved to be a lower possibility measure and an upper necessity measure. Similarly, it is shown that any anti-capacity (i.e., a decreasing set function) can be viewed both as an upper guaranteed possibility measure and as a lower weak necessity measure. These results are the basis for establishing that qualitative integrals (including Sugeno integrals) are lower and /or upper possibilistic expectations wrt a possibility measure, while qualitative desintegrals are upper or lower possibilistic expectations wrt a guaranteed possibility measure. The results are presented in a finite qualitative setting, and apply to multiple criteria aggregation or decision under uncertainty.