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The paper builds upon a recent approach to find the approximate bounds of areal function using Polynomial Chaos expansions. Given a function of randomvariables with compact support probability distributions, the intuition is toquantify the uncertainty in the response using Polynomial Chaos expansion anddiscard all the information provided about the randomness of the output andextract only the bounds of its compact support. To solve for the bounding rangeof polynomials, we transform the Polynomial Chaos expansion in the Bernsteinform, and use the range enclosure property of Bernstein polynomials to find theminimum and maximum value of the response. This procedure is used to propagateDempster-Shafer structures on closed intervals through nonlinear functions andit is applied on an algebraic challenge problem.

Approximate Interval Method for Epistemic Uncertainty Propagation using Polynomial Chaos and Evidence Theory