This paper is devoted to the construction of sets of joint probability measures for the case that the marginal sets of probability measures are generated by weighted focal sets. Different conditions on the choice of the weights of the joint focal sets and on the probability measures on these sets lead to different types of independence such as strong independence, random set independence, fuzzy set independence and unknown interaction. As an application the upper probabilities of failure of a beam are computed.
Keywords. Weighted focal sets, random sets, possibility measures, plausibility measures, lower and upper probabilities, sets of probability measures
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