Mixed aleatory and epistemic uncertainty quantification using fuzzy set theory

• Propose an uncertainty representation technique for modeling mixed types of uncertainty using the concept of fuzzy probabilities.
• Discuss the requirements of fuzzy probabilities for uncertainty representation in an ensemble.
• Demonstrate the properties of proposed uncertainty representation technique in both one-dimensional and high-dimensional examples.
• Apply the proposed uncertainty representation technique to isocontour extraction.

This paper proposes algorithms to construct fuzzy probabilities to represent or model the mixed aleatory and epistemic uncertainty in a limited-size ensemble. Specifically, we discuss the possible requirements for the fuzzy probabilities in order to model the mixed types of uncertainty, and propose algorithms to construct fuzzy probabilities for both independent and dependent datasets. The effectiveness of the proposed algorithms is demonstrated using one-dimensional and high-dimensional examples. After that, we apply the proposed uncertainty representation technique to isocontour extraction, and demonstrate its applicability using examples with both structured and unstructured meshes.