Quantification of various types of uncertainty in biological computational models using fuzzy mass functions.

We develop a unified uncertainty propagation framework for computational models involving stochastic variability together with two distinct forms of epistemic uncertainty: vagueness and incomplete knowledge. In this framework, stochastic uncertainty is represented by random variables, while the epistemic components are modeled by random fuzzy sets with fuzzy mass functions generalized from Dempster-Shafer theory and fuzzy set theory. Using generalized polynomial chaos expansions and extension principles, the propagated uncertainty in output expectation is then quantified efficiently by a fuzzy mass function. We also introduce a distance measure between fuzzy mass functions and use it to analyze the error in the resulting numerical approximations. The proposed approach is demonstrated on several simple examples and applied to two biological systems: the Mitchell-Schaeffer model governed by a system of ordinary differential equations, and a computational model of olfaction governed by the Navier-Stokes equations.