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

Isai Chavarri; Yanyan He; Minyi Chen; John W. Cain; Lindsay Waldrop; Isai Chavarri; Yanyan He; Minyi Chen; John W. Cain; Lindsay Waldrop

doi:10.3934/mbe.2026081

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 8: 2228-2258. doi: 10.3934/mbe.2026081

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Research article

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

1.
Department of Mathematics, University of North Texas, 1155 Union Circle, Denton 76203, TX, USA
2.
Department of Mathematics, and of Computer Science and Engineering, University of North Texas, 1155 Union Circle, Denton 76203, TX, USA
3.
Department of Mathematics, Harvard University, One Oxford Street, Cambridge 02138, MA, USA
4.
Schmid College of Science and Technology, Chapman University, One University Drive, Orange 92866, CA, USA

Received: 28 April 2026 Revised: 08 June 2026 Accepted: 07 July 2026 Published: 21 July 2026

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.
- fuzzy sets,
- fuzzy mass function,
- generalized polynomial chaos,
- Dempster-Shafer theory,
- Mitchell-Schaeffer model,
- olfaction
Citation: Isai Chavarri, Yanyan He, Minyi Chen, John W. Cain, Lindsay Waldrop. Quantification of various types of uncertainty in biological computational models using fuzzy mass functions[J]. Mathematical Biosciences and Engineering, 2026, 23(8): 2228-2258. doi: 10.3934/mbe.2026081

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Abstract

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.

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