An approach to modelling and simulation of uncertain dynamical systems. (English) Zbl 1232.68131

Hüllermeier, Eyke

Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5, No. 2, 117-137 (1997).

Summary: Coping with uncertainty in dynamical systems has recently received some attention in artificial intelligence (AI), particularly in the fields of qualitative and model-based reasoning. In this paper, we propose an approach to modelling and simulation of uncertain dynamics which is based on the following ideas: We consider (linguistic) descriptions of uncertain functional relationships characterizing the behavior of some dynamical system. Based on a certain interpretation of such rule-based models, we derive a fuzzy function \(\widetilde F\). It is shown that all (reasonable) fuzzy functions can be approximated to any degree of accuracy in this way. The function \(\widetilde F\) is then used as the “fuzzy” right-hand side of a set of differential equations, which leads us to consider fuzzy initial value problems. We propose an interpretation of such problems. Moreover, several aspects of simulation methods for characterizing the set of all system behaviors compatible with this interpretation are discussed.

MSC:

68T37	Reasoning under uncertainty in the context of artificial intelligence
34A07	Fuzzy ordinary differential equations
93A30	Mathematical modelling of systems (MSC2010)

Keywords:

linguistic modelling; fuzzy functions; approximation; dynamical systems; fuzzy differential equations; reachable sets