Random set theory and problems of modeling
SIAM Review
The mean value of a fuzzy number
Fuzzy Sets and Systems - Fuzzy Numbers
Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference
Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference
Decision Making with Monotone Lower Probabilities of Infinite Order Fabrice
Mathematics of Operations Research
Imprecise distribution function associated to a random set
Information Sciences—Informatics and Computer Science: An International Journal
A random set characterization of possibility measures
Information Sciences—Informatics and Computer Science: An International Journal
On topological properties of the Choquet weak convergence of capacity functionals of random sets
Information Sciences: an International Journal
Choquet weak convergence of capacity functionals of random sets
Information Sciences: an International Journal
Random intervals as a model for imprecise information
Fuzzy Sets and Systems
A random set description of a possibility measure and its natural extension
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Upper and lower probabilities induced by a fuzzy random variable
Fuzzy Sets and Systems
Upper and lower probabilities induced by a fuzzy random variable
Fuzzy Sets and Systems
Mark-recapture techniques in statistical tests for imprecise data
International Journal of Approximate Reasoning
On the fusion of imprecise uncertainty measures using belief structures
Information Sciences: an International Journal
Eliciting dual interval probabilities from interval comparison matrices
Information Sciences: an International Journal
Characterizing joint distributions of random sets by multivariate capacities
International Journal of Approximate Reasoning
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A random set can be regarded as the result of the imprecise observation of a random variable. Following this interpretation, we study to which extent the upper and lower probabilities induced by the random set keep all the information about the values of the probability distribution of the random variable. We link this problem to the existence of selectors of a multi-valued mapping and with the inner approximations of the upper probability, and prove that under fairly general conditions (although not in all cases), the upper and lower probabilities are an adequate tool for modelling the available information. In doing this, we generalise a number of results from the literature. Finally, we study the particular case of consonant random sets and we also derive a relationship between Aumann and Choquet integrals.