Verified stochastic methods

Markov set-chains and dependency modeling of mean and standard deviation

authored by: Gabor Rebner, Michael Beer, Ekaterina Auer, Matthias Stein
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.
External Organisation(s): University of Liverpool
University of Duisburg-Essen
National University of Singapore
Type: Article
Journal: Soft Computing
Volume: 17
Pages: 1415-1423
No. of pages: 9
ISSN: 1432-7643
Publication date: 08.2013
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Software, Theoretical Computer Science, Geometry and Topology
Electronic version(s): https://doi.org/10.1007/s00500-013-1009-7 (Access: Closed)