r-bounded fuzzy measures are equivalent to ε-possibility measures

Traditional probabilistic description of uncertainty is based on additive probability measures. To describe non-probabilistic uncertainty, it is therefore reasonable to consider non-additive measures. An important class of non-additive measures are possibility measures, for which μ(A ∪ B) = max(μ(A), μ(B)). In this paper, we show that possibility measures are, in some sense, universal approximators: for every ε > 0, every non-additive measure which satisfies a certain reasonable boundedness property is equivalent to a measure which is ε-close to a possibility measure.