The mean value of a fuzzy number
Fuzzy Sets and Systems - Fuzzy Numbers
Random sets and fuzzy interval analysis
Fuzzy Sets and Systems - Special issue on mathematical aspects of fuzzy sets
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Simulation and the Monte Carlo Method
Simulation and the Monte Carlo Method
Uncertainty-Based Information: Elements of Generalized Information Theory
Uncertainty-Based Information: Elements of Generalized Information Theory
Statistical Modeling, Analysis and Management of Fuzzy Data
Statistical Modeling, Analysis and Management of Fuzzy Data
A random set characterization of possibility measures
Information Sciences—Informatics and Computer Science: An International Journal
Uncertainty and Information: Foundations of Generalized Information Theory
Uncertainty and Information: Foundations of Generalized Information Theory
An Introduction to Copulas (Springer Series in Statistics)
An Introduction to Copulas (Springer Series in Statistics)
Some properties of a random set approximation to upper and lower distribution functions
International Journal of Approximate Reasoning
Representing parametric probabilistic models tainted with imprecision
Fuzzy Sets and Systems
Joint Propagation and Exploitation of Probabilistic and Possibilistic Information in Risk Assessment
IEEE Transactions on Fuzzy Systems
International Journal of Approximate Reasoning
Representation theorem for probabilities on IFS-events
Information Sciences: an International Journal
Fuzzy structural analysis based on fundamental reliability concepts
Computers and Structures
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Random set theory is a useful tool to quantify lower and upper bounds on the probability of the occurrence of events given uncertain information represented for example by possibility distributions, probability boxes, or Dempster-Shafer structures, among others. In this paper it is shown that the belief and plausibility estimated by Dempster-Shafer evidence theory are basically approximations by Riemann-Stieltjes sums of the integrals of the lower and upper probability employed when using infinite random sets of indexable type. In addition, it is shown that the evaluation of the lower and upper probability is more efficient if it is done by pseudo-Monte Carlo strategies. This discourages the use of Dempster-Shafer evidence theory and suggests the use of infinite random sets of indexable type specially in high dimensions, not only because the initial discretization step of the basic variables is not required anymore, but also because the evaluation of the lower and upper probability of events is much more efficient using the different techniques for multidimensional integration like Monte Carlo simulation.