The mean value of a fuzzy number
Fuzzy Sets and Systems - Fuzzy Numbers
Focusing versus updating in belief function theory
Advances in the Dempster-Shafer theory of evidence
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
A random set characterization of possibility measures
Information Sciences—Informatics and Computer Science: 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
Hi-index | 0.00 |
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. Finally, we study the particular case of consonant random sets and we also derive a relationship between Aumann and Choquet integrals.