This article is devoted to the propagation of families of confidence intervals obtained by non-parametric methods through multivariate functions comprising the semantics of confidence limits. At fixed confidence level, local random sets are defined whose aggregation admits the calculation of upper probabilities of events. In the multivariate case, a number of ways of combinations is highlighted to encompass independence and unknown interaction using random set independence and Fr\'echet bounds. For all cases we derive formulas for the corresponding upper probabilities and elaborate how they relate. The methods are exemplified by means of an example from structural mechanics.
Keywords. Confidence intervals, non-parametric models of uncertainty, random sets, fuzzy sets, upper probability, independence, unknown interaction, Fr\'echet bounds
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Institut für Grundlagen der Bauingenieurwissenschaften, AB Technische Mathematik,
Technikerstraße 13, Innsbruck