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Erschienen in:
01.08.2013 | Focus
Verified stochastic methods
Markov set-chains and dependency modeling of mean and standard deviation
Erschienen in: Soft Computing | Ausgabe 8/2013
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Abstract
Markov chains provide quite attractive features for simulating a system’s behavior under consideration of uncertainties. However, their use is somewhat limited because of their deterministic transition matrices. Vague probabilistic information and imprecision appear in the modeling of real-life systems, thus causing difficulties in the pure probabilistic model set-up. Moreover, their accuracy suffers due to implementations on computers with floating point arithmetics. Our goal is to address these problems by extending the Dempster-Shafer with Intervals toolbox for MATLAB with novel verified algorithms for modeling that work with Markov chains with imprecise transition matrices, known as Markov set-chains. Additionally, in order to provide a statistical estimation tool that can handle imprecision to set up Markov chain models, we develop a new verified algorithm for computing relations between the mean and the standard deviation of fuzzy sets.