Aggregation of Possibility Measures

Possibility measures are not closed under convex combinations, since the nestedness property of focal sets is not preserved under this aggregation mode. This paper intends to investigate the eventwise aggregations of possibility measures that preserve the consonance property of these set-functions. It is proved that these operations are defined as the union (via the maximum) of some monotonic pointwise transformations of the fuzzy sets that characterize the possibility measures ; especially the previously introduced weighted maximum operations are among the natural solutions. This work also suggests to view a fuzzy set as a disjunctive aggregation of possibly dissonant imprecise, individual opinions, the weights reflecting the degrees of membership of individuals in the group. The extension of these results to decomposable set-functions is considered.

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