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This paper presents a methodology for developing grey models of process systems, that is, models that, being based on fundamental principles and laws of nature, combine them with sub-models obtained from experimental data. The method follows two steps: the first one takes advantage of what is known, while the second uses the data and mixed-integer optimization algorithms to identify the structure and parameters of the remaining parts of the model. The method is illustrated in a challenging biotechnological process: the Acetone-Butanol-Ethanol (ABE) fermentation process.

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In this contribution, we revisit Zadeh's Extension Principle in the context of imprecise probabilities and present two simple modifications to obtain meaningful results when using possibilistic calculus to propagate credal sets of probability distributions through models. It is demonstrated how these results facilitate the possibilistic solution of two benchmark problems in uncertainty quantification.