Verified stochastic methods

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

verfasst von

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.

Externe Organisation(en)

The University of Liverpool
Universität Duisburg-Essen
National University of Singapore

Typ

Artikel

Journal

Soft Computing

Band

17

Seiten

1415-1423

Anzahl der Seiten

9

ISSN

1432-7643

Publikationsdatum

08.2013

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Software, Theoretische Informatik, Geometrie und Topologie

Elektronische Version(en)

https://doi.org/10.1007/s00500-013-1009-7 (Zugang: Geschlossen)