Abstract
Probability and possibility theory deal with different types of uncertainty. The paper discusses the role of these formalisms in the simulation of continuous dynamical systems where parameters and/or initial conditions are uncertain.
We derive analytically the evolution law of possibility distributions in continuous dynamical system and we compare it with consolidated results in probability theory. The analysis illustrates the limits of conventional Monte Carlo techniques for the simulation of dynamical systems where the uncertainty is expressed in a non probabilistic form. We show that the interaction existing between the probability distribution and the dynamics of the system may produce, in some cases, an inaccurate outcome of the Monte Carlo simulation, making then advisable the adoption of an appropriate possibilistic technique.
Also, we propose a new algorithm for the numerical simulation of a differential system, where the uncertainty of parameters and/or initial conditions is represented by fuzzy distributions. Finally, we discuss the simulation of a dynamical system where the evolution of the possibilistic uncertainty is simulated by using both probabilistic and possibilistic techniques.
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Bontempi, G. (2004). Simulating continuous dynamical systems under conditions of uncertainty: the probability and the possibility approaches. In: Nikravesh, M., Zadeh, L.A., Korotkikh, V. (eds) Fuzzy Partial Differential Equations and Relational Equations. Studies in Fuzziness and Soft Computing, vol 142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39675-8_4
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DOI: https://doi.org/10.1007/978-3-540-39675-8_4
Publisher Name: Springer, Berlin, Heidelberg
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