title: Fuzzy Stochastic Petri Nets for Modeling Biological Systems with Uncertain Kinetic Parameters.
abstract: Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability), which has prevented a wider application of SPNs that require accurate parameters. Considering the strength of fuzzy sets to deal with uncertain information, we apply a specific type of stochastic Petri nets, fuzzy stochastic Petri nets (FSPNs), to model and analyze biological systems with uncertain kinetic parameters. FSPNs combine SPNs and fuzzy sets, thereby taking into account both randomness and fuzziness of biological systems. For a biological system, SPNs model the randomness, while fuzzy sets model kinetic parameters with fuzzy uncertainty or variability by associating each parameter with a fuzzy number instead of a crisp real value. We introduce a simulation-based analysis method for FSPNs to explore the uncertainties of outputs resulting from the uncertainties associated with input parameters, which works equally well for bounded and unbounded models. We illustrate our approach using a yeast polarization model having an infinite state space, which shows the appropriateness of FSPNs in combination with simulation-based analysis for modeling and analyzing biological systems with uncertain information.
authors.affiliation: Control and Simulation Center, Harbin Institute of Technology, Harbin, 150080 China.
authors.forename: Fei
authors.initials: F
authors.lastname: Liu
authors.affiliation: Department of Computer Science, Brandenburg University of Technology Cottbus-Senftenberg, Cottbus, 03013 Germany.
authors.forename: Monika
authors.initials: M
authors.lastname: Heiner
authors.affiliation: Control and Simulation Center, Harbin Institute of Technology, Harbin, 150080 China.
authors.forename: Ming
authors.initials: M
authors.lastname: Yang
mesh_terms: D017143:Fuzzy Logic; D008954:Models, Biological; D013269:Stochastic Processes