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Let (X, A) be a fixed measurable space and two monotone measures μ1 and μ2 two monotone measures defined on A, we consider the pseudo-addition μ1 ⊕ μ2 of these two monotone measures. It is a new monotone measure λ. Such a monotone measure is absolutely continuous with respect to μ1 and μ2. Not only that, the new monotone measure preserves most of desirable structural characteristics of the monotone...
Given a measurable space (X, A) and two fuzzy measures μ1 and μ2 defined on A, the addition of μ1 and μ2 determines another set function on A. Such a new set function is a fuzzy measure, too. We shall discuss the relation between the new fuzzy measure and the original fuzzy measures. We shall see that the new fuzzy measure preserves some structural characteristics, such as subadditivity, several kinds...
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